# Statistics for Decision Making

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**Statistics for Decision Making**

Create a histogram for the variable Height. You need to create a frequency distribution for…

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## Statistics for Decision Making

Statistics for Decision Making

**MATH 221 A+ Entire NEW Course: Homework Week 1-7| Lab Week 2, 4, 6| Quiz Week 3, 5, 7| Reflection Paper Week 8| Discussions Week 1-7 | Final Exam**

All quizzes include formulas.

**MATH 221 Lab Week 2**

**https://www.hiqualitytutorials.com/product/math221-lab-week-2/**

Name: _______________________

Statistical Concepts that you will learn after completing this Lab:

- Using Excel for Statistics
- Graphics
- Descriptive Statistics
- Empirical Rule
- Data have already been formatted and entered into an Excel worksheet.
- Obtain the Lab data file (Excel) for this lab from your instructor.
- Use the Week 1 spreadsheet (available from Week 1: Resources) for graphs and calculations. You will need to copy data from the Lab data file into the Week 1 calculations spreadsheet to answer some of these Lab questions.
- The names of each variable from the survey are in the first row of the Lab data Worksheet. This row has a double-underline to identify the heading row as the variable names. All other rows of the Worksheet represent a certain students’ answers to the survey questions. Therefore, the rows are called observations and the columns are called variables. On the last page of this Week 2 Lab document, you will find a Code Sheet section that identifies the correspondence between the variable names and the survey questions.
- Follow the directions below and then paste the graphs from Excel into the gray response areas for question 1 through 3. You will be using the Week 1 Excel Sheet for many of the calculations. Type your answers to questions 4 through 11 where noted in the gray areas. When asked for explanations, please give thorough, multi-sentence or paragraph length explanations.
- The completed Lab Word Document with your responses to the 11 questions will be the ONE and only document submitted to the Week 2: Lab. When saving and submitting the document, you are required to use the following filename format, replacing “Your_Name_Here” with your “Last name_First name”:

__Creating Graphs__

- Create a pie chart for the variable Car Color: Select the column with the Car variable, including the title of Car Color. Click on Insert, and then Recommended Charts. It should show a clustered column and click OK. Once the chart is shown, right click on the chart (main area) and select Change Chart Type. Select Pie and OK. Click on the pie slices, right click Add Data Labels, and select Add Data Callouts. Add an appropriate title.

2. Create a histogram for the variable Height. You need to create a frequency distribution for the data by hand. Use 5 classes, find the class width, and then create the classes. Once you have the classes, count how many data points fall within each class. It may be helpful to sort the data based on the Height variable first. Once you have the classes and the frequency counts, put those data into the table in the Freq Distribution worksheet of the Week 1 Excel file.* *Copy and paste the graph here.

3. Create a scatter plot with the variables of height and money. Copy the height variable from the data file and paste it into the x column in the Scatter Plot worksheet of the week 1 Excel file. Copy the money variable from the data file and paste it into the y column. Copy and paste the scatter plot below.

Calculating Descriptive Statistics

- Calculate descriptive statistics for the variable Height by Gender. Sort the data by gender by clicking on Data and then Sort. Copy the heights of the males form the data file into the Descriptive Statistics worksheet of the week 1 Excel file. Type the standard deviations below. These are sample data. Then from the data file, copy and paste the female data into the Descriptive Statistics workbook and do the same

Mean | Standard deviation | |

Females | ||

Males |

__Short Answer Writing Assignment__

All answers should be complete sentences.

- What is the most common color of car for students who participated in this survey? Explain how you arrived at your answer.

6. What is seen in the histogram created for the heights of students in this class (include the shape)? Explain your answer.

7. What is seen in the scatter plot for the height and money variables? Explain your answer.

8. Compare the mean for the heights of males and the mean for the heights of females in these data. Compare the values and explain what can be concluded based on the numbers.

9. Compare the standard deviation for the heights of males and the standard deviation for the heights of females in the class. Compare the values and explain what can be concluded based on the numbers.

10. Using the empirical rule, 95% of female heights should be between what two values? Either show work or explain how your answer was calculated.

11. Using the empirical rule, 68% of male heights should be between what two values? Either show work or explain how your answer was calculated.

__Code Sheet__

Do __NOT__ answer these questions.

The Code Sheet just lists the variables name and the question used by the researchers on the survey instrument that produced the data that are included in the data file. This is just information. The first question for the lab is after the code sheet.

Variable Name | Question |

Drive | Question 1 – How long does it take you to drive to the school on average (to the nearest minute)? |

State | Question 2 – What state/country were you born? |

Temp | Question 3 – What is the temperature outside right now? |

Rank | Question 4 – Rank all of the courses you are currently taking. The class you look most forward to taking will be ranked one, next two, and so on. What is the rank assigned to this class? |

Height | Question 5 – What is your height to the nearest inch? |

Shoe | Question 6 – What is your shoe size? |

Sleep | Question 7 – How many hours did you sleep last night? |

Gender | Question 8 – What is your gender? |

Race | Question 9 – What is your race? |

Car | Question 10 – What color of car do you drive? |

TV | Question 11 – How long (on average) do you spend a day watching TV? |

Money | Question 12 – How much money do you have with you right now? |

Coin | Question 13 – Flip a coin 10 times. How many times did you get tails? |

Die1 | Question 14 – Roll a six-sided die 10 times and record the results. |

Die2 | |

Die3 | |

Die4 | |

Die5 | |

Die6 | |

Die7 | |

Die8 | |

Die9 | |

Die10 |

Statistics for Decision Making

**MATH 221 Lab Week 4**

**https://www.hiqualitytutorials.com/product/math221-lab-week-4/**

Name: _______________________

Statistical Concepts:

- Probability
- Binomial Probability Distribution

Calculating Binomial Probabilities

NOTE: For question 1, you will be using the same data file your instructor gave you for the Week 2 Lab.

- Using the data file from your instructor (same one you used for the Week 2 Lab), calculate descriptive statistics for the variable (Coin) where each of the thirty-five students in the sample flipped a coin 10 times. Round your answers to three decimal places and type the mean and the standard deviation in the grey area below.

Mean: Standard deviation: |

NOTE: for questions 2-7, you will NOT be using the data file your instructor gave you. Please follow the instructions given in each question.

__Plotting the Binomial Probabilities__

- For the next part of the lab, open the Week 3 Excel worksheet. This will be used for the next few questions, rather than the data file used for the first question.

- Click on the “binomial tables” workbook
- Type in n=10 and p=0.5; this simulates ten flips of a coin where x is counting the number of heads that occur throughout the ten flips
- Create a scatter plot, either directly in this spreadsheet (if you are comfortable with those steps), or by using the Week 1 spreadsheet and copying the data from here onto that sheet (x would be the x variable, and P(X=x) would be the y variable.
- Repeat steps 2 and 3 with n=10 and p=0.25
- Repeat steps 2 and 3 with n=10 and p=0.75
- In the end, you will have three scatter plots for the first question below.
- Create scatter plots for the binomial distribution when p=0.50, p=0.25, and p=0.75 (see directions above). Paste the three scatter plots in the grey area below.

__Calculating Descriptive Statistics__

__Short Answer Writing Assignment – Both the calculated binomial probabilities and the descriptive statistics from the class database will be used to answer the following questions. Round all numeric answers to three decimal places.__

- List the probability value for each possibility in the binomial experiment
__calculated at the beginning of this lab__, which was calculated with the probability of a success being ½. (Complete sentences not necessary; round your answers to three decimal places.)

P(x=0) | P(x=6) | |||

P(x=1) | P(x=7) | |||

P(x=2) | P(x=8) | |||

P(x=3) | P(x=9) | |||

P(x=4) | P(x=10) | |||

P(x=5) |

4. Give the probability for the following based on the calculations __in question 3 above__, with the probability of a success being ½. (Complete sentences not necessary; round your answers to three decimal places.)

P(x≥1) | P(x<0) | |||

P(x>1) | P(x≤4) | |||

P(4<x ≤7) | P(x<4 or x≥7) |

5. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ½ and n = 10. Either show your work or explain how your answer was calculated. Use these formulas to do the hand calculations: Mean = *np*, Standard Deviation =

Mean = np:Standard Deviation = : |

6. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¼ and n = 10. Write a comparison of these statistics to those from question 5 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = *np*, Standard Deviation =

Mean = np:Standard Deviation = : Comparison: |

7. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¾ and n = 10. Write a comparison of these statistics to those from question 6 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = *np*, Standard Deviation =

Mean = np:Standard Deviation = : Comparison: |

NOTE: For questions 8-9, you will use the results of the previous questions.

- Using all four of the properties of a Binomial experiment (see page 201 in the textbook) explain in a short paragraph of several complete sentences why the Coin variable from the class survey represents a binomial distribution from a binomial experiment.

9. Compare the mean and standard deviation for the Coin variable (question 1) with those of the mean and standard deviation for the binomial distribution that was calculated by hand in question 5. Explain how they are related in a short paragraph of several complete sentences.

Mean from question #1: Standard deviation from question #1: Mean from question #5: Standard deviation from question #5: Comparison and explanation: |

Statistics for Decision Making

**MATH 221 Lab Week 6**

**https://www.hiqualitytutorials.com/product/math221-ilab-week-6/**

Name:_______________________

Statistical Concepts:

- Data Simulation
- Confidence Intervals
- Normal Probabilities

__Short Answer Writing Assignment__

All answers should be complete sentences.

We need to find the confidence interval for the SLEEP variable. To do this, we need to find the mean and standard deviation with the Week 1 spreadsheet. Then we can the Week 5 spreadsheet to find the confidence interval.

First, find the mean and standard deviation by copying the SLEEP variable and pasting it into the Week 1 spreadsheet. Write down the mean and the sample standard deviation as well as the count. Open the Week 5 spreadsheet and type in the values needed in the green cells at the top. The confidence interval is shown in the yellow cells as the lower limit and the upper limit.

- Give and interpret the 95% confidence interval for the hours of sleep a student gets.

Change the confidence level to 99% to find the 99% confidence interval for the SLEEP variable.

- Give and interpret the 99% confidence interval for the hours of sleep a student gets.

3. Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs.

In the Week 2 Lab, you found the mean and the standard deviation for the HEIGHT variable for both males and females. Use those values for follow these directions to calculate the numbers again.

(From Week 2 Lab: Calculate descriptive statistics for the variable Height by Gender. Click on Insert and then Pivot Table. Click in the top box and select all the data (including labels) from Height through Gender. Also click on “new worksheet” and then OK. On the right of the new sheet, click on Height and Gender, making sure that Gender is in the Rows box and Height is in the Values box. Click on the down arrow next to Height in the Values box and select Value Field Settings. In the pop up box, click Average then OK. Write these down. Then click on the down arrow next to Height in the Values box again and select Value Field Settings. In the pop up box, click on StdDev then OK. Write these values down.

You will also need the number of males and the number of females in the dataset. You can either use the same pivot table created above by selecting Count in the Value Field Settings, or you can actually count in the dataset.

Then use the Week 5 spreadsheet to calculate the following confidence intervals. The male confidence interval would be one calculation in the spreadsheet and the females would be a second calculation.

- Give and interpret the 95% confidence intervals for males and females on the HEIGHT variable. Which is wider and why?

5. Give and interpret the 99% confidence intervals for males and females on the HEIGHT variable. Which is wider and why?

6. Find the mean and standard deviation of the DRIVE variable by copying that variable into the Week 1 spreadsheet. Use the Week 4 spreadsheet to determine the percentage of data points from that data set that we would expect to be less than 40. To find the actual percentage in the dataset, sort the DRIVE variable and count how many of the data points are less than 40 out of the total 35 data points. That is the actual percentage. How does this compare with your prediction?

Mean ______________ Standard deviation ____________________ Predicted percentage ______________________________ Actual percentage _____________________________ Comparison ___________________________________________________ ___________________________________________________________ |

7. What percentage of data would you predict would be between 40 and 70 and what percentage would you predict would be more than 70 miles? Use the Week 4 spreadsheet again to find the percentage of the data set we expect to have values between 40 and 70 as well as for more than 70. Now determine the percentage of data points in the dataset that fall within this range, using same strategy as above for counting data points in the data set. How do each of these compare with your prediction and why is there a difference?

Predicted percentage between 40 and 70 ______________________________ Actual percentage _____________________________________________ Predicted percentage more than 70 miles ________________________________ Actual percentage ___________________________________________ Comparison ____________________________________________________ ______________________________________________________________ Why? __________________________________________________________ ________________________________________________________________ |

**MATH 221 Refection Paper Week 8**

**https://www.hiqualitytutorials.com/product/math-221-refection-paper/**

Complete the following by writing a response to __three__ of the four following questions. For each question, your response should be 2 or more paragraphs. Make it clear which question you are answering and use correct grammar throughout. If you answer all four questions, only the first three provided will be graded.

Your responses are to be based on your own experiences and insights. Do not use materials and examples from other sources, including the Internet. Students have used examples from outside sources in the past and have failed this final assessment and in some cases, failed the course due to evidence of plagiarism.

- Describe how you could use
__hypothesis testing__to help make a decision in your current job, a past job, or a life situation. Include a description of the decision, what would be the null and alternative hypotheses, and how data could ideally be collected to test the hypotheses. - Describe how you could use
__confidence intervals__to help make a decision in your current job, a past job, or life situation. Include a description of the decision, how the interval would impact the decision, and how data could ideally be collected to determine the interval. - Describe how you could use
__regression analysis__to help make a decision in your current job, a past job, or a life situation. Include a description of the decision, what would be the independent and dependent variables, and how data could ideally be collected to calculate the regression equation. - Describe a data set that you have encountered or could envision that would be applicable to your current job, a past job, or a life situation. Identify two (2) options for
__graphically representing__those data to present to decision-makers, such a pie charts, time series, Pareto charts, histograms, etc. Assess the pros and cons of each graphical option.

Category | Points | % | Description |

First question response | 42 | 28% | Is the statistical approach applied in a relevant situation? Are subsequent questions answered? |

Second question response | 42 | 28% | Is the statistical approach applied in a relevant situation? Are subsequent questions answered? |

Third question response | 42 | 28% | Is the statistical approach applied in a relevant situation? Are subsequent questions answered? |

Content Organization and Cohesiveness | 12 | 8% | Is the paper clear, concise, are ideas presented and developed, does the paper flow? How easy/difficult is the paper to read? |

Grammar, Spelling, Editing, and so on | 12 | 8% | Is the paper of high quality, few or no misspelled words, correct grammar and punctuation used, and so on? |

Total | 150 | 100% | A quality paper will meet or exceed all of the above requirements. |

Statistics for Decision Making

**MATH 221 Quiz Week 3**

**https://www.hiqualitytutorials.com/product/math221-quiz-week-3/**

**Question 1**

**(CO 1) A survey of 1272 pre-owned vehicle shoppers found that 8% bought the extended warranties. What is the population and what is the sample?**

Population: 1272 pre-owned Vehicle shoppers; Sample: the 8% that bought extended warranties

Population: 1272 pre-owned Vehicle shoppers; Sample: pre-owned vehicle shoppers

Population: pre-owned vehicle shoppers; Sample: the 8% that bought extended warranties

Population: pre-owned vehicle shoppers; Sample: 1272 pre-owned vehicle shoppers

**Question 1**

**A survey of 128 DeVry statistics students found that 83% read the announcements each week. What is the population and what is the sample?**

Population: DeVry statistics students; sample: the 83% that read the announcements weekly

Population: all statistics students; Sample 128: DeVry statistics students

Population: DeVry statistics students: Sample: 128 DeVry Statistics students

Population: all statistics students reading announcements weekly; Sample: the 128 DeVry statistics students

**Question 1**

**Among 500 people at the concert, a survey of 35 found 28% found it too loud. What is the population and what is the sample?**

Population: 500 at that concert; sample: the 35 in the survey

Population: all concert goers; sample: the 28% who found it too loud

Population: 500 at that concert: Sample: the 28% who found it too loud

Population: all concert goers; Sample: the 500 at that concert

**Question 2**

**(CO 1) A survey of 481 of your customers shows that 79% of them like the recent changes to the product. Is this percentage a parameter or a statistic and why?**

Statistics as it represents the population

Parameter as it represents the sample

Statistic as it represents the sample

Parameter is it represents the population

Statistics for Decision Making

**Question 2**

**The measurements of 100 products from the assembly line show that 99% are correct. Is this percentage a parameter or a statistic and why?**

Parameter as it represents the sample

Statistic as it represents the sample

Parameter as it represents the population

Statistic as it represents the population

**Question 2**

**The measurements of 100 products from the assembly line show that 99% are correct. Is this percentage a parameter or a statistic and why?**

Parameter as it represents the sample

Statistic as it represents the sample

Parameter as it represents the population

Statistic as it represents the population

**Question 3**

**In asking all 349 second graders in a school district, it is found that on average, these second graders have 2.5 pets. Is this number a parameter or a statistic and why?**

Statistic as it represents the population

Statistic as it represents the sample

Parameter as it represents the population

Parameter as it represents the sample

**Question 3**

**Classify the data of the top grossing movies for 2017.**

Qualitative

Quantitative

Classical

Statistics

**Question 3**

**Classify the data of the heights of ladders produced by a tool company.**

Qualitative

Statistics

Classical

Quantitative

Statistics for Decision Making

**Question 4**

**The data set that lists the number of performances for each Broadway show in 2017 would be classified as what type of data?**

Ordinal

Ratio

Nominal

Interval

**Question 4**

**The data set that lists the runs scored at each of the weekend’s baseball games would be classified as what type of data?**

Interval

Ratio

Nominal

Ordinal

**Question 4**

**The data set that lists the temperatures in Albany NY each day in the month of February would be classified as what type of data?**

Ratio

Ordinal

Nominal

Interval

**Question 5**

**A data set that includes the values given by customers to determine their level of satisfaction with their purchases. The scale used is very satisfied, somewhat satisfied, somewhat dissatisfied, and very dissatisfied. The data of the customer responses would be classified as what type of data?**

Ratio

Nominal

Ordinal

Interval

Statistics for Decision Making

**Question 5**

**A data set that includes the number of products that were produced within each hour by a company would be classified as what type of data?**

Nominal

Ratio

Interval

Ordinal

**Question 5**

**A data set that includes the years in which your hometown team won championships would be classified as what type of data:**

Ordinal

Nominal

Interval

Ratio

**Question 6**

**What type of data collection might be best to estimate the impact of exercise on longevity?**

Observational

Survey

Experiment

Simulation

Statistics for Decision Making

**Question 6**

**What type of data collection might be best to estimate the amount of time individuals spend socializing?**

Simulation

Experiment

Survey

Observational

**Question 7**

**What type of data collection might be best to study how many books students bring into the media center during finals week?**

Simulation

Survey

Observational

Experiment

**Question 7**

**What type of data collection might be best to study how voters might decide an upcoming ballot issue?**

Experiment

Survey

Simulation

Observational

**Question 8.**

**You need to study the satisfaction of customers of a specific restaurant. You decide to order food and talk to those customers sitting next to you. This would most closely describe which type of sampling technique?**

Convenience

Systematic

Stratified

Random

**Question 8**

**You need to study the satisfaction of customers of a specific restaurant. You ask every 10 ^{th} customer as they leave after their meal. This would most closely describe which type of sampling technique?**

Systematic

Stratified

Convenience

Random

**Question 8**

**You need to study the satisfaction of customers of a specific restaurant. You ask every 10 ^{th} customer as they leave after their meal. This would most closely describe which type of sampling** technique?

Systematic

Convenience

Random

Stratified

Statistics for Decision Making

**Question 9**

**Which of the following graphs would be a histogram?**

**Question 9**

**Which of the following graphs would be a dot plot?**

**Question 9**

**Which of the following graphs would be a line graph?**

**Question 10**

**In a normally distributed data set of how long customers stay in your store, the mean is 31.7 minutes and the standard deviation is 1.9 minutes. Within what range would you expect 95% of your customers to stay in your store?**

30.75-32.7

26.0-37.4

29.8-33.6

27.9-35.5

Statistics for Decision Making

**Question 10**

**In a normally distributed data set of how long customers stay in your store, the mean is 50.3 minutes and the standard deviation is 3.6 minutes. Within what range would you expect 95% of your customers to stay in your store?**

39.5-61.1

43.1-57.5

46.7-53.9

48.5-52.1

**Question 11**

**Which of the following graphs would be considered right skewed?**

**Question 11**

**Which of the following graphs would be considered normally distributed?**

Graph 1

Graph 2

Graph 3

Graph 4

**Question 11**

**Which of the following graphs would be considered normally distributed?**

**Question 12**

**In a normally distributed data set with a mean of 19 and a standard deviation of 2.6, what percentage of the data would be 13.8 and 24.2?**

68% based on the histogram

95% based on the histogram

95% based on the empirical rule

68% based on the empirical rule

**Question 12**

**In a normally distributed data set with a mean of 22 and a standard deviation of 4.1, what % of the data would be between 13.8 and 30.2**

95% based on the histogram

68% based on the histogram

68% based on empirical rule

95% based on empirical rule

**Question 12**

**In a normally distributed data set with a mean of 22 and a standard deviation of 4.1, what percentage of data would be between 17.9 and 26.1?**

99.7% based on empirical rule

68% based on the histogram

68% based on the empirical rule

95% based on the empirical rule

**Question 13**

**Which of the following would be the standard deviation for this sample data set: 5,7,3,9,2,4,4,9,5,9,3?**

5.45

2.50

2.62

2.73

Statistics for Decision Making

**Question 13**

**Which of the following would be the standard deviation for this sample data set: 5,7,6,9,4,4,6,5,2,5?**

2.68

1.72

5.36

1.80

**Question 13**

**Which of the following would be the standard deviation for this sample data set: 5,7,3,9,2,4,4,9,5,9,3**

2.73

5.45

2.50

2.62

**Question 14**

**What would be the mean of this data set? 8,9,7,451,7,1,5,3,4?**

27.5

55.0

55.3

75.3

**Question 14**

**What would be the mean of this data set: 8,9,7,508,7,.1,5,8,1?**

33.8

50.8

5.8

61.6

Statistics for Decision Making

**Question 15**

**A pharmaceutical company wants to determine If its new medicine helps heal bruises more quickly than not treating the bruise. What type of study would be best suited to make this determination?**

Simulation

Experimental

Survey

Observational

**Question 15**

**A city wants to know how many cars come to a complete stop at the stop signs in downtown? What type of study would be best suited to make this determination?**

Observational

Simulation

Experimental

Survey

**Question 16**

**To gather information on customer satisfaction, a researcher goes into several stores and interviews randomly selected customers. This sampling technique is called:**

Stratified

Convenience

Random

Cluster

**Question 16**

**To gather information on customer satisfaction, a researcher goes into the local store and interviews six randomly selected customers. This sampling technique is called:**

Stratified

Random

Cluster

Convenience

Statistics for Decision Making

**Question 16**

**To gather information on customer satisfaction, a researcher randomly selects four store locations and interviews all the customers at those selected stores. This sampling technique is called:**

Convenience

Stratified

Cluster

Random

**Question 17**

**What is the standard deviation and its meaning given this population of customer ages? 45,76,30,22,51,40,63,66,41?**

17.5 which means that many of the ages will be around the square of this value

16.5 which means that many of the ages will be around this value

17.5 which means that many of the ages will be within this value of the average age

16.5 which means that many of the ages will be within this value of the average age

**Question 17**

**What is the standard deviation and its meaning given the population of customer ages? 45, 76, 30, 22, 24, 40, 63, 66, and 27**

20.2 which means that many of the ages will be around the square of this value

19.0 which means that many of the ages will be around this value

20.2 which means that many of the ages will be within this value of the average age

19.0 which means that many of the ages will be within this value of the average age

**Question 18**

**A random selection from a deck of cards selects one card. What is the probability of selecting an ace?**

0.025

0.250

0.50

0.077

**Question 18**

**A random number generator is used to select a number from 1 to 100. What is the probability of selecting an even number?**

0.25

0.95

0.50

0.005

Statistics for Decision Making

**Question 18**

**A random number generator is used to select a number from 1 to 100. What is the probability of selecting an even number?**

0.005

0.25

0.95

0.50

**Question 19**

**What is the sample space to responses to a question whose answers are Yes or No, along with a question on location with possible answers of North, South, East, or West?**

Yes no north south east west

Yes yes no no north north south south east east west west

Yes north yes south yes east yes west yes no no north no south no east no west

Yes north yes south yes east yes west no north no south no east no west

**Question 19**

**What is the sample space to responses to a question whose answers are up, down, left or right along with a question on preference between blue and red?**

Up blue up red down blue down red left blue left red right blue right red

Up blue up blue down blue down blue left blue left blue right blue right blue

Up up down down left left right right blue blue red red

Up down left right blue red

Statistics for Decision Making

**Question 20**

**Consider the table below**

Response (number of cats owned | Frequency

None | 659

One | 329

Two | 52

Three | 13

Four or more | 8

What is the probability that the next person asked only has two cats?

5%

31%

62%

50%

**Question 20**

**Consider the table below**

Response (number of cats owned) | Frequency |

None | 659 |

One | 329 |

Two | 52 |

Three | 13 |

Four or more | 8 |

What is the probability that the next person asked has only one cat?

62%

50%

5%

31%

**Question 21**

**Consider the table below**

Age group | Frequency

18-29 | 9831

30-39 | 7845

40-49 | 6869

50-59 | 6323

60-69 | 5410

70 and over | 5279

23.7%

42.5%

28.2%

31.7%

Statistics for Decision Making

**Question 21**

**Consider the table below**

Age group | Frequency |

18-29 | 9831 |

30-39 | 7845 |

40-49 | 6869 |

50-59 | 6323 |

60-69 | 5410 |

70 and over | 5279 |

What is the probability that the next person chosen will be in the 18-29 or 30-39 age groups?

23.7%

37.8%

42.5%

18.9%

**Question 22**

**According to company records, the probability that a dishwasher will need repairs during its first six years is 0.09. this is an example of which type of probability?**

Empirical probability

Public probability

Subjective probability

Classical probability

**Question 22**

**When children roll a die for a game, their probability of rolling a 5 is 17%. This is an example of which type of probability?**

Empirical probability

Public probability

Classical probability

Subjective probability

**Question 23**

**Consider the table below:**

Age group | frequency

18-29 | 9831

30-39 | 7845

40-49 | 6869

50-59 | 6323

60-69 | 5410

70 and over | 5279

What is p (40-59’)?

68.3

31.7

64.6

71.8

Statistics for Decision Making

**Question 23**

**Consider the table below.**

71.8%

25.7%

64.6%

74.3%

**Question 23**

**Consider the table below.**

Age group | Frequency |

18-29 | 9831 |

30-39 | 7845 |

40-49 | 6869 |

50-59 | 6323 |

60-69 | 5410 |

70 and over | 5279 |

What is P(50-69’)?

76.3%

64.6%

68.3%

71.8%

Statistics for Decision Making

**Question 24**

**You are selling your product at a 3 day event. Each day, there is a 60% chance that you will make money. What is the probability that you will make money all three days?**

0.288

0.216

0.096

0.144

**Question 25**

**Consider the table below.**

Profit | Loss | Total | |

Urban location | 50 | 38 | 88 |

Rural location | 61 | 84 | 125 |

Total | 111 | 132 | 243 |

Find the probability that a randomly selected location is going to be profitable, given that it is in an urban location.

36.2

56.8

48.8

51.4

**Question 25**

36.2%

28.8%

55.0%

48.8%

**Question 25**

**Consider the table below.**

Profit | Loss | Total | |

Urban Location | 50 | 38 | 88 |

Rural Location | 61 | 84 | 125 |

Total | 111 | 132 | 243 |

Find the probability that a randomly selected location is going to be profitable, given that it is in an urban location.

48.8%

36.2%

51.4%

56.8%

Statistics for Decision Making

**Question 26**

**Consider the table below:**

**Find the probability that a random selected product is from the north, given that it is correct.**

87.2

88.9

12.1

36.4

**Question 26**

**Consider the table below.**

**Find the probability that a random selected product is defective, given that it is from the south production facility.**

10.7%

12.8%

13.1%

23.7%

**Question 26**

**Consider the table below.**

Production location | Correct | Defective | Total |

East | 258 | 31 | 289 |

West | 572 | 106 | 678 |

NORTH | 755 | 94 | 849 |

SOUTH | 491 | 74 | 565 |

TOTAL | 2076 | 305 | 2381 |

34.8%

84.4%

28.5%

15.6%

**Question 27**

**Classify these events. Selecting a king from a deck of cards, replacing it and selecting a queen from the same deck. These events would be considered:**

Independent

Empirical

Subjective

Dependent

Statistics for Decision Making

**Question 27**

**Classify these events. Selecting a king from a deck of cards, keeping it and selecting another king from the same deck. These events would be considered:**

Dependent

Independent

Subjective

Empirical

**Question 28**

**Classify these events. Some of the businesses have large stores and some businesses have large parking lots. These events would be considered:**

Subjective

Independent

Dependent

Classical

**Question 28**

**Classify these events. A study found that people who suffer from stress are more likely to have health issues. These events would be considered**

Dependent

Subjective

Independent

Classical

Statistics for Decision Making

**Question 29**

**In a survey of 331 customers, 66 say that service is poor. You select two customers without replacement to get more information on their satisfaction. What is the probability that both say service is poor?**

3.93

19.70

3.88

4.00

**Question 29**

**In a survey of 320 customers, 58 say that service is poor. You select two customers without replacement to get more information on their satisfaction. What is the probability that both say service is poor?**

3.20%

3.24%

3.19%

3.29%

**Question 29**

**In a survey of 320 customers, 84 say that service is poor. You select two customers without replacement to get more information on their satisfaction. What is the probability that both say service is poor?**

6.83%

6.81%

6.89%

21.25%

**Question 30**

**Randomly select a customer that takes the bus to our store. Randomly select a customer that is a teenage. Are these events mutually exclusive?**

Mutually exclusive events

Non-mutually exclusive events

Statistics for Decision Making

**Question 30**

**Randomly select a customer that purchases tofu. Randomly select a customer that purchases chicken. Are these events mutually exclusive?**

Mutually exclusive events

Non-mutually exclusive events

**MATH 221 Quiz Week 5**

**https://www.hiqualitytutorials.com/product/math221-quiz-week-5/**

**Question 1**

**(CO 3) Consider the following table**

Age Group Frequency

18-29 983

30-39 784

40-49 686

50-59 632

60-69 541

70 and over 527

If you created the probability distribution for these data, what would be the probability of 60-69?

0.165

0.157

0.127

0.130

Statistics for Decision Making

**Question 2**

**(CO 3) Consider the following table of hours worked by part-time employees. These employees must work in 5 hour blocks.**

Weekly Hours Worked Probability

5 0.06

15 0.18

20 0.61

25 0.15

**Question 3**

**(CO 3) Consider the following table.**

Defects in batch Probability

- 30
- 28
- 21
- 09
- 08
- 04

Find the variance of this variable

1.99

0.67

1.49

1.41

**Question 4**

**(CO 3) Consider the following table**

Defects in batch Probability

- 04
- 11
- 25
- 20
- 19
- 21

Find the standard deviation of this variable.

1.44

2.08

1.41

3.02

Statistics for Decision Making

**Question 5**

**(CO 3) Twenty-two percent of US teens have heard of a fax machine. You randomly select 12 US teens. Find the probability that the number of these selected teens that have of a fax machine is exactly six (first answer listed below). Find the probability that the number is more than 8 (second answer below)**

0.024, 0.001

0.993, 0.024

0.993, 0.000

0.024, 0.000

**Question 6**

**(CO 3) Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 7 of the 10 have the right shape, should the company stop the production line?**

Yes, as the probability of seven having the correct shape is not unusual

Yes, as the probability of seven having the correct shape is unusual

No, as the probability of seven having the correct shape is unusual

No, as the probability of seven having the correct shape is not unusual

**Question 7**

**(CO 3) A bottle of water is supposed to have 20 ounces. The bottling company has determined that 98% of bottles have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 36 has all bottles properly filled?**

N=20, p=36, x=98

N=36, p=0.98, x=36

N=36, p=0.98, x=1

N=0, p=0.98, x=36

Statistics for Decision Making

**Question 8**

**(CO 3) On the production line the company finds that 85.6% of products are made correctly. You are responsible for quality control and take batches of 30 products from the line and test them. What number of the 30 being incorrectly made would cause you to shut down production?**

Less than 26

Less than 23

Less than 25

Less than 24

**Question 9**

**(CO 3) The probability of someone ordering the daily special is 52%. If the restaurant expected 65 people for lunch, how many would you expect to order the daily special? **

35

30

31

34

**Question 10**

**(CO 3) Forty-seven percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?**

0, 1, 7, 8

0, 1, 2, 8

0, 1, 2, 8

1, 2, 8

**Question 11**

**(CO 3) Eighty-four percent of products come off the line ready to ship to distributors. Your quality control department selects 12 products randomly from the line each hour. Looking at the binomial distribution, if fewer than how many are within specifications would require that the production line be shut down (unusual) and repaired?**

Fewer than 6

Fewer than 7

Fewer than 8

Fewer than 9

**Question 12**

**(CO 3) Out of each 100 products, 93 are ready for purchase by customers. If you selected 27 products, what would be the expected (mean) number that would be ready for purchase by customers?**

27

25

26

24

Statistics for Decision Making

**Question 13**

**(CO 3) Sixty-seven percent of adults have looked at their credit score in the past six months. If you select 31 customers, what is the probability that at least 25 of them have looked at their score in the past six months?**

0.030

0.970

0.073

0.043

**Question 14**

**(CO 3) One out of every 92 tax returns that a tax auditor examines requires an audit. If 50 returns are selected at random, what is the probability that less than 3 will need an audit?**

0.0151

0.0109

0.9978

0.9828

Question 15

**(CO 3) Thirty-eight percent of consumers prefer to purchase electronics online. You randomly select 16 consumers. Find the probability that the number who prefers to purchase electronics online is at most 3. **

0.088

0.912

0.027

0.380

Statistics for Decision Making

**Question 16**

**(CO 3) The speed of cars on a stretch of road is normally distributed with an average 40 miles per hour with a standard deviation of 5.9 miles per hour. What is the probability that a randomly selected car is violating the speed limit of 50 miles per hour?**

0.10

0.95

0.05

0.59

**Question 17**

**(CO 3) A survey indicates that shoppers spend an average of 22 minutes with a standard deviation of 16 minutes in your store and that these times are normally distributed. Find the probability that a randomly selected shopper will spend less than 20 minutes in the store.**

0.45

0.37

0.55

0.20

**Question 18**

**(CO 3) The monthly utility bills in a city are normally distributed with a mean of $121 and a standard deviation of $41. Find the probability that a randomly selected utility bill is between $110 and $130.**

0.606

0.193

0.394

0.336

**Question 19**

**(CO 3) A restaurant serves hot chocolate that has a mean temperature of 175 degrees with a standard deviation of 8.1 degrees. Find the probability that a randomly selected cup of hot chocolate would have a temperature of less than 164 degrees. Would this outcome warrant a replacement cup (meaning that it would be unusual)?**

Probability of 0.09 and would not warrant a refund

Probability of 0.91 and would not warrant a refund

Probability of 0.91 and would warrant a refund

Probability of 0.09 and would warrant a refund

Statistics for Decision Making

**Question 20**

**(CO 3) The yearly amounts of carbon emissions from cars in Belgium are normally distributed with a mean of 13.9 gigagrams per year. Find the probability that the amount of carbon emissions from cars in Belgium for a randomly selected year are between 11.5 gigagrams and 14.0 gigagrams per year.**

0.107

0.397

0.496

0.603

**Question 21**

**(CO 3) On average, the parts from a supplier have a mean of 97.5 inches and a standard deviation of 12.2 inches. Find the probability that a randomly selected part from this supplier will have a value between 87.5 and 107.5 inches. Is this consistent with the Empirical Rule of 68%-95%-99%.7?**

Probability is 0.68, which is consistent with the Empirical Rule

Probability us 0.79, which is inconsistent with the Empirical Rule

Probability is 0.95, which is consistent with the Empirical Rule

Probability is 0.59, which is inconsistent with the Empirical Rule

**Question 22**

**(CO 3) A process is normally distributed with a mean of 104 rotations per minute and a standard deviation of 8.2 rotations per minute. If a randomly selected minute has 128 rotations per minute, would the process be considered in control or out of control?**

Out of control as this one data point is more than two standard deviations from the mean

In control as only one data would be outside the allowable range

In control as this one data point is not more than three standard deviations from the mean

Out of control as this one data point is more than three standard deviation from the mean

**Question 23**

**(CO 3) The soup produced by a company has a salt level that is normally distributed with a mean of 5.4 grams and a standard deviation of 0.3 grams. The company takes readings of every 10 ^{th} bar off the production line. The reading points are 5.8, 4.9, 5.2, 5.0, 4.9, 6.2, 5.1, 6.7, 6.1. Is the process or out of control and why?**

It is out of control as one of these data points is more than 3 standard deviation from the mean

It is in control as the values jump above and below the mean

It is in control as the data points more than 2 standard deviation from the mean are far apart

It is out of control as two of these data points are more than 2 standard deviations from the mean

Statistics for Decision Making

**Question 24**

**(CO 3) The blenders produced by a company have a normally distributed life span with a mean of 8.2 years and a standard deviation of 1.3 years. What warranty should be provided so that the company is replacing at most 6% of their blenders sold?**

- years

6.9 years

6.2 years

10.2 years

**Question 25**

**(CO 3) A puck company wants to sponsor the players with the 10% quickest goals in hockey games. The times of first goals are normally distributed with a mean of 8.54 minutes and a standard deviation of 4.91 minutes. How fast would a player need to make a goal to be sponsored by the puck company?**

7.92 minutes

14.83 minutes

2.25 minutes

9.16 minutes

**Question 26**

**(CO 3) A stock’s price fluctuations are approximately normally distributed with a mean of $104.50 and a standard deviation of $20.88. Yu decide to purchase whenever the price reaches its lowest 20% of values. What is the most you would be willing to pay for the stock?**

$83.62

$122.07

$110.48

$86.93

**Question 27**

**(CO 3) The times that customers spend in a book store are normally distributed with a mean of 39.5 minutes and a standard deviation of 9.4 minutes. A random sample of 25 customers has a mean of 36.1 minutes or less. Would this outcome be considered unusual, so that he store should reconsider its displays?**

No, the probability of this outcome at 0.359 would be considered usual, so there is no problem

Yes, the probability of this outcome at 0.965 would be considered unusual, so the display should be redone

Yes, the probability of this outcome at 0.035, would be considered unusual, so the display should be redone

No, the probability of this outcome at 0.035, would be considered usual, so there is no problem

**Question 28**

**(CO 3) The weights of ice cream cartons are normally distributed with a mean weight of 20.1 ounces and a standard deviation of 0.3 ounces. You randomly select 25 cartons. What is the probability that their mean weight is greater than 20.06 ounces? **

0.553

0.748

0.252

0.447

Statistics for Decision Making

**Question 29**

**(CO 3) Recent test scores on the Law School Admission Test (LSAT) are normally distributed with a mean of 162.4 and a standard deviation of 10.7. What is the probability that the mean of 8 randomly selected scores is less than 161?**

0.350

0.356

0.552

0.448

**Question 30**

**(CO 3) The mean annual salary for intermediate level executives is about $74000 per year with a standard deviation of $2500. A random sample of 36 intermediate level executives is selected. What is the probability that the mean annual salary of the sample is between $71000 and $74000?**

0.500

0.603

0.385

0.452

**MATH 221 Quiz Week 7**

**https://www.hiqualitytutorials.com/product/math221-quiz-week-7/**

**Questions 1**

**(CO 4) From a random sample of 55 businesses, it is found that the mean time that employees spend on persona issues each week is 5.8 hours with a standard deviation of 0.35 hours. What is the 95% confidence interval for the amount of time spent on personal issues?**

(5.72, 5.88)

(5.73, 5.87)

(5.74, 5.90)

(5.71, 5.89)

Statistics for Decision Making

**Question 2**

**(CO 4) If a confidence interval is given from 8.56 to 10.19 and the mean is known to be 9.375, what is the margin of error?**

1.630

8.560

0.408

0.815

**Question 3**

**(CO 4) Which of the following is most likely to lead to a large margin of error?**

Small sample size

Small mean

Small standard deviation

Large sample size

**Question 4**

**(CO 4) From a random sample of 41 teens, it is found that on average they spend 31.8 hours each week online with a population standard deviation of 5.91 hours. What is the 90% confidence interval for the amount of time they spend online each week?**

(30.62, 32.99)

(30.28, 33.32)

(29.99, 33.61)

(25.89, 37.71)

**Question 5**

**(CO 4) A company making refrigerators strives for the internal temperature to have a mean of 37.5 degrees with a population standard deviation of 0.6 degrees, based on samples of 100. A sample of 100 refrigerators have an average temperature of 37.37 degrees. Are the refrigerators within the 90% confidence interval? **

No, the temperature is outside the confidence interval of (36.90, 38.10)

Yes, the temperature is within the confidence interval of (37.40, 37.60)

Yes, the temperature is within the confidence interval of (36.90, 38.10)

No, the temperature is outside the confidence interval of (37.40, 37.60)

**Question 6**

**(CO 4) What is the 97% confidence interval for a sample of 104 soda cans that have a mean amount of 12.10 ounces and a population standard deviation of 0.08 ounces?**

(12.035, 12.065)

(12.033, 12.067)

(12.020, 12.180)

(12.083, 12.117)

**Question 7**

**(CO 4) Determine the minimum sample size required when you want to be 98% confident that the sample mean is within two units of the population mean. Assume a population standard deviation of 5.75 in a normally distributed population.**

45

23

44

43

Statistics for Decision Making

**Question 8**

**(CO 4) Determine the minimum sample size required when you want to be 80% confident that the sample mean is within 1.5 units of the population mean. Assume a population standard deviation of 9.24 in a normally distributed population.**

63

62

145

146

**Question 9**

**(CO 4) Determine the minimum sample size required when you want to be 75% confident that the sample mean is within twenty-five units of the population mean. Assume a population standard deviation of 327.8 in a normally distributed population.**

661

283

466

228

**Question 10**

**(CO 4) In a sample of 8 high school students, they spent an average of 28.8 hours each week doing sports with a sample standard deviation of 3.2 hours. Find the 95% confidence interval, assuming the times are normally distributing.**

(25.62, 32.48)

(22.47, 35.21)

(26.12, 31.48)

(24.10, 34.50)

**Question 11**

**(CO 4) In a sample of 15 stuffed animals, you find that they weigh an average of 8.56 ounces with a sample standard deviation of 0.08 ounces. Find the 92% confidence interval, assuming the times are normally distributed.**

(8.528, 8.591)

(8.543, 8.577)

(8.516, 8.604)

(8.521, 8.599)

Statistics for Decision Making

**Question 12**

**(CO 4) Market research indicates that a new product has the potential to make the company an additional $3.8 million, with a standard deviation of $1.8 million. If this estimate was based on a sample of 10 customers from a normally distributed data set, what would be the 90% confidence interval?**

(2.51, 5.09)

(2.00, 5.60)

(3.06, 4.54)

(2.76, 4.84)

**Question 13**

**(CO 4) Supplier claims that they are 95% confident that their products will be in the interval of 20.45 to 21.05. You take samples and find that the 95% confidence interval of what they are sending is 20.02 to 21.48. What conclusion can be made?**

The supplier products have a lower mean than claimed

The supplier products have a higher mean than claimed

The supplier more accurate than they claimed

The supplier is less accurate than they have claimed

**Question 14**

**(CO 4) In a sample of 19 small candles, the weight is found to be 3.72 ounces with a standard deviation of 0.963 ounces. What would be the 87% confidence interval for the size of the candles, assuming the data are normally distributed?**

(3.337, 4.103)

(3.199, 4.241)

(3.369, 4.071)

(3.371, 4.069)

**Question 15**

**(CO 4) In a situation where the population standard deviation was known rather than the sample standard deviation, what would be the impact on the confidence interval?**

It would become narrower with fewer values

It would remain the same as standard deviation does not impact confidence intervals

It would become wider due to using the z distribution

It would become narrower due to using the z distribution

Statistics for Decision Making

**Question 16**

**(CO 4) A company claims that its heaters last at most 5 years. Write the null and alternative hypotheses and note which is the claim.**

Ho: µ≤5, Ha: µ > 5 (claim)

Ho: µ>5 (claim), Ha: µ ≤ 5

Ho: µ=5 (claim), Ha: µ ≥5

Ho: µ≤5 (claim), Ha: µ >5

**Question 17**

**(CO 4) An executive claims that her employees spend no less than 2.5 hours each week in meetings. Write the null and alternative hypotheses and note which is the claim.**

Ho: µ≥2.5 (claim), Ha: µ <2.5

Ho: µ≤2.5 (claim), Ha: µ <2.5

Ho: µ=2.5, Ha: µ ≥2.5 (claim)

Ho: µ>2.5, Ha: µ ≤2.5 (claim)

**Question 18**

**(CO 5) In hypothesis testing, a key element in the structure of the hypotheses is that the claim is ___________**

The alternative hypothesis

The null hypothesis

Either one of the hypotheses

Both hypothesis

**Question 19**

**(CO 5) A landscaping company claims that at least 90% of workers arrive on time. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted?**

There is sufficient evidence to support the claim that a least 90% of workers arrive on time

There is sufficient evidence to support the claim that more than 90% workers arrive on time

There is not sufficient evidence to support the claim that more than 90% of workers arrive on time

There is not sufficient evidence to support the claim that at least 90% of workers arrive on time

**Question 20**

**(CO 5) A textbook company claims that their book is so engaging that less than 55% of students read it. If a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted?**

There is sufficient evidence to support the claim that less than 55% of students read this text

There is not sufficient evidence to support the claim that no more than 55% of students read this text

There is sufficient evidence to support the claim that no more than 55% of students read this text

There is not sufficient evidence to support the claim that less than 55% of students read this text

Statistics for Decision Making

**Question 21**

**(CO 5) An advocacy group claims that the mean braking distance of a certain type of tire is 75 feet when the car is going 40 miles per hour. In a test of 80 of these tires, the braking distance has a mean of 77 and a population standard deviation of 5.9 feet. Find the standardized test statistic and the corresponding p-value.**

z-test statistic = 3.03, p-value = 0.0024

z-test statistic = -3.03, p-value = 0.0024

z-test statistic = -3.03, p-value = 0.0012

z-test statistic = 3.03, p-value = 0.0012

**Question 22**

**(CO 5) The heights of 82 coasters have a mean of 284.9 feet and a population standard deviation of 59.3 feet. Find the standardized tests statists and the corresponding p-value when is that roller coasters are less than 290 feet tall.**

z-test statistic = -0.78, p-value – 0.4361

z-test statistic = 0.78, p-value – 0.4361

z-test statistic = 0.78, p-value – 0.2181 5

z-test statistic = -0.78, p-value – 0.2181

**Question 23**

**(CO 5) A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 720 hours. A random sample of 51 light bulbs as a mean of 701.6 hours with a population standard deviation of 62 hours. At an ɑ=0.05, can you support the company’s claim using the test statistics?**

Claim is the null, fail to reject the null and cannot support claim as test statistic (-2.12) is not in the rejection region defined by the critical value (-1.645)

Claim is the alternative, fail to reject the null and cannot support claim as the test statistic (-2.12) is in the rejection region defined by the critical value (-1.96)

Claim is the alternative, reject the null and support claim as test statistic (-2.12) is not in the rejection region defined by the critical value (-1.96)

Claim is the null, reject the null and cannot support claim as test statistic (-2.12) is in the rejection region defined by the critical value (-1.645)

Statistics for Decision Making

**Question 24**

**(CO 5) A restaurant claims the customers receive their food in less than 16 minutes. A random sample of 39 customers finds a mean wait time for food to be 15.8 minutes with a population standard deviation of 4.9 minutes. At ɑ = 0.04, can you support the organizations’ claim using the test statistic?**

Claim is the alternative, fail to reject the null so cannot support the claim as test statistic (-0.25) is not in the rejection region defined by the critical value (-1.75)

Claim is the null, fail to reject the null so support the claim as test statistic (-0.25) is not in the rejection region defined by the critical value (-1.75)

Claim is the alternative, reject the null so support the claim as test statistic (-0.25) is in the rejection region defined by the critical value (-2.05)

Claim is the null, reject the null so cannot support the claim as test statistic (-0.25) is in the rejection region defined by the critical value (-2.05)

**Question 25**

**(CO 5) A manufacturer claims that their calculators are 6.800 inches long. A random sample of 39 of their calculators finds they have a mean of 6.812 inches with a population standard deviation of 0.05 inches. At ɑ=0.08, can you support the manufacturer’s claim using the p value?**

Claim is the null, fail to reject the null and support claim as p-value (0.134) is greater than alpha (0.08)

Claim is the alternative, reject the null and cannot support claim as p-value (0.134) is greater than alpha (0.08)

Claim is the alternative, fail to reject the null and support claim as p-value (0.067) is less than alpha (0.08)

Claim is the null, reject the null and cannot support claim as p-value (0.067) is less than alpha (0.08)

**Question 26**

**(CO 5) A travel analyst claims that the mean room rates at a three-star hotel in Chicago is greater than $152. In a random sample of 36 three-star hotel rooms in Chicago, the mean room rate is $163 with a population standard deviation of $41. At ɑ=0.10, can you support the analysist’s claim using the p-value?**

Claim is the alternative, reject the null as p-value (0.054) is less than alpha (0.10), and can support the claim

Claim is the null, rejects the null as p-value (0.054) is less than alpha (0.10), and cannot support the claim

Claim is the null, fail to reject the null as p-value (0.054) is less than alpha (0.10), and cannot support the claim

Claim is the alternative, fail to reject the null as p-value (0.054) is less than alpha (0.10), and can support the claim

Statistics for Decision Making

**Question 27**

**(CO 5) A car company claims that the mean gas mileage for its luxury sedan is at least 24 miles per gallon. A random sample of 7 cars has a mean gas mileage of 23 miles per gallon and a standard deviation of 3.5 miles per gallon. At ɑ=0.05, can you support the company’s claim assuming the population is normally distributed?**

No, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported

Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported

Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported

Question 28

(CO 5) A state department of Transportation claims that the mean wait time for various services at its different location is more than 6 minutes. A random sample of 16 services at different locations has a mean wait time of 9.5 minutes and a standard deviation of 7.6 minutes. At ɑ=0.05, can the department’s claim be supported assuming the population is normally distributed?

No, since p of 0.043 is greater than 0.05, fail to reject the null. Claim is alternative, so is not supported

Yes, since p of 0.043 is less than 0.05, reject the null. Claim is alternative, so is supported

Yes, since p of 0.043 is greater than 0.05, fail to reject the null. Claim is null, so is supported

No, since p of 0.043 is greater than 0.05, reject the null. Claim is null, so is not supported

**Question 29**

**(CO 5) A used car dealer says that the mean price of a three-year-old sport utility vehicle in good condition is $18,000. A random sample of 20 such vehicles has a mean price of $18,450 and a standard deviation of $1860. At ɑ=0.08, can the dealer’s claim be supported assuming the population is normally distributed?**

Yes, since the test statistic of 1.08 is in the rejection region defined by the critical value of 1.46, the null is rejected. The claim is the null, so is supported

Yes, since the test statistic of 1.08 is not in the rejection region defined by the critical value of 1.85, the null is not rejected. The claim is the null, so is supported

No, since the test statistic of 1.08 is in the rejection region defined by the critical value of 1.85, the null is rejected. The claim is the null, so is not supported

No, since the test statistic of 1.08 is close to the critical value of 1.24, the null is not rejected. The claim is the null, so is supported

**Question 30**

**(CO 5) A researcher wants to determine if eating more vegetables helps high school juniors learn algebra. A junior class is divided into pairs and one student from each pair has extra vegetables and the other in the pair does not. After 2 weeks, the entire class takes an algebra test and the results of the two groups are compared. To be a valid matched pair test, what should the researcher consider in creating the two groups?**

That each pair of students has similar IQs or abilities in mathematics

Than the group without extra vegetables receives different instruction

That each pair of students has similar ages at the time of the testing

That the group with the extra vegetables also has more sweets

Statistics for Decision Making

**MATH 221 Homework Week 1**

**https://www.hiqualitytutorials.com/product/math221-homework-week-1/**

**Question 1**

**A recent survey of the alumni of a university indicated that the average salary of 10,000 of its 200,000 graduates was $130,000. The $130,000 would be considered a:**

Population

Sample

Statistic

Parameter

**Question 2**

**Of all DeVry students, a study found that 43% of them are business majors. The 43% would be considered a:**

Parameter

Sample

Statistic

Population

**Question 3**

**The average age of students in a statistics class is 28 years. The 28 years would be considered an example of:**

Qualitative data

Inferential statistics

Descriptive statistics

A population

**Question 4**

**The ages of 20 first graders would be considered:**

Quantitative data

Nominal data

Qualitative data

Interval data

Statistics for Decision Making

**Question 5**

**The ratings of 50 movies would be considered:**

Ratio data

Quantitative data

Interval data

Ordinal data

**Question 6**

**The final grades for students in a statistics class would be considered:**

Interval data

Ordinal data

Nominal data

Ratio data

**Question 7**

**A researcher randomly selects and interviews fifty male and fifty female teachers. This sampling technique is called:**

Convenience

Stratified

Random

Cluster

**Question 8**

**A personnel director at a large company would like to determine whether the company cafeteria is widely used by employees. She calls each employee and asks them whether they usually bring their own lunch, eat at the company cafeteria, or go out for lunch. This study design would be considered:**

Simulation

Survey

Observational

Experimental

**Question 9**

**Which of the following would be the mean of this data set: 5, 7, 12, 36, 14, 12, 33, 21**

17.5

11.6

11.6

13.00

Statistics for Decision Making

**Question 10**

**Which of the following would be the standard deviation of this sample data set: 67, 54, 30, 77, 61, 41, 75, 83**

17.3

61.0

18.4

340.3

**Question 11**

**Which of the following would be the variance of this population data set: 3, 6, 8, 9, 4, 5, 7, 1, 9, 7, 5, 4, 13, 9**

8.82

9.49

2.97

12.00

**Question 12**

**If a data set is right skewed, where would the mean be in relation to the mode?**

At a lower value

At the same value

At a higher value

Right skewed distributions don’t have a mean nor mode

Statistics for Decision Making

**Question 13**

**If data set A has a larger mean than data set B, what would be different about their distributions?**

The distribution of data set A would generally be to the left of the distribution of data set B

The distribution of data set A would generally be to the right of the distribution of data set B

Data set A would have flatter distribution with more data in each tail

Data set A would have more data near the center of the distribution

**Question 14**

**In a normally distributed data set with a mean of 24 and a standard deviation of 4.2, what percentage of the data would be between 15.6 and 32.4 and why?**

68% based on the Empirical Rule

68% based on the histogram

95% based on the histogram

95% based on the Empirical Rule

**Question 15**

**Which of the following data sets would you expect to have the highest standard deviation?**

Weight of an orange (in ounces)

Ages of people taking college classes (in years)

Amount of soda in an unopened can (in ounces)

The number of phones a person owns

**Question 16**

**Which data outcome of the number of customers in line would best support opening another cash register?**

Low mean with small standard deviation

High mean with high standard deviation

High mean with small standard deviation

Low mean with high standard deviation

**Question 17**

**In manufacturing, systematic sampling could be used to determine if the machines are operating correctly. Which of the following best describes this type of sampling?**

Products are put into groups and some are randomly selected from each group

Every 10th product in the line is selected

Products are put into groups and all are included from several randomly selected groups

Samples are randomly selected throughout the day

Statistics for Decision Making

**Question 18**

**A graph shows a number line with a mark for each data value in the data set above its value. This graphic is most likely to be:**

A frequency histogram

A dot plot

A stem-leaf plot

A frequency polygon

**Question 19**

**Match the terms and their definitions**

Vertical bar chart that shows frequency on the y-axis

A sample where the population is divided into groups and several groups are randomly selected from all from those selected groups are sampled

Collection of all counts that are of interest

A subset or part of a population

A sample where the population is divided into groups and several are randomly sampled form each group

Consists of attributes, labels, or nonnumerical entries

**Question 20**

**Match the terms and their definitions**

The most frequent number appearing in a dataset

The average

The percentage of data that falls within 1, 2, or 3 standard deviations of the mean in a symmetrical, bell-shaped distribution

The square root of the variance

Show how far a particular data point is from the mean in terms of the number of standard deviations

Statistics for Decision Making

**MATH 221 Homework Week 2**

**https://www.hiqualitytutorials.com/product/math221-homework-week-2/**

**Question 1**

**The probability of drawing one card and getting queen is 4/52. This would be considered:**

Classical probability

Manufactured probability

Subjective probability

Empirical probability

**Question 2**

**Given the following information, find the probability that a randomly selected student will be tall, but not very tall. Number of students who are very short: 45, short: 60, tall: 82, very tall: 21**

50.5%

39.4%

49.5%

10.1%

**Question 3**

**Given the following information, find the probability that a randomly selected dog will be a golden retriever or a poodle. Number of dogs who are poodles: 31, golden retrievers: 58, beagles: 20, pugs: 38**

39.5%

58.0%

60.5%

46.9%

**Question 4**

**Given that there is a 21% chance it will rain on any day, what is the probability that it will rain on the first day and be clear (not rain) on the next two days?**

13.1%

16.6%

36.2%

21.0%

Statistics for Decision Making

**Question 5**

**Consider the following table. What is the probability of red?**

Red | Blue | Total | |

Yes | 15 | 21 | 36 |

No | 38 | 13 | 51 |

Total | 53 | 34 | 87 |

53/87

15/53

36/87

15/87

**Question 6**

**Consider the following table. What is probability of yes, given green?**

Red | Blue | Green | Total | |

Yes | 33 | 44 | 14 | 91 |

No | 18 | 5 | 28 | 51 |

Total | 51 | 49 | 42 | 142 |

42/142

14/42

51/142

14/91

**Question 7**

**A card is randomly selected from a standard deck of 52 cards. What is P(face card)?**

12/52

26/52

4/52

13/52

Statistics for Decision Making

**Question 8**

**In a sample of 400 customers, 140 say that service is poor. You select two customers without replacement to get more information on their satisfaction. What is the probability that both say service is poor?**

12.25%

12.19%

35.00%

65.00%

**Question 9**

**In a sample of 587 customers, 308 say they are happy with the service. If you select three customers without replacement for a commercial, what is the probability they will all say they are happy with the service?**

52.47%

14.45%

14.38%

27.53%

**Question 10**

**One event is a father being right handed. The other event is that his daughter is right handed. How would you classify these events?**

Independent

Dependent

**Question 11**

**A company sells 14 types of crackers that they label varieties 1 through 14, based on spice level. What is the probability that one purchase results in a selection of a cracker with an even number or a number less than 5?**

71.4%

35.7%

64.3%

14.0%

**Question 12**

**Of the shirts produced by a company, 5.5% have loose threads, 8.5% have crooked stitching, and 3.5% have loose threads and crooked stitching. Find the probability that a randomly selected shirt has loose threads or has crooked stitching.**

17.5%

10.5%

14.0%

12.0%

Statistics for Decision Making

**Question 13**

**Randomly select a customer that is happy with the company. Randomly select a customer who is elderly. Are these events mutually exclusive?**

Mutually exclusive events

Non-mutually exclusive events

**Question 14**

**In a sample of 800 adults, 242 said that they liked sugar cereals. Three adults are selected at random without replacement. Find the probability that all three like sugar cereals.**

2.77%

2.73%

2.74%

2.70%

**Question 15**

**In a sample of 80 adults, 25 said that they would buy a car from a friend. Three adults are selected at random without replacement. Find the probability that none of the three would buy a car from a friend.**

2.80%

32.50%

31.93%

25.80%

**Question 16**

**A sock drawer has 17 folded pairs of socks, with 7 pairs of white, 6 pairs of black and 4 pairs of blue. What is the probability, without looking in the drawer, that you will first select and remove a black pair, then select either a blue or a white pair?**

35.25%

64.71%

24.26%

22.84%

**Question 17**

**An investment advisor believes that there is a 28% chance of making money by investing in a specific stock. If the stock makes money, then there is a 43% chance that among those making money, they would also get a dividend. Find the probability that the investor makes money and receive a dividend.**

28%

15%

43%

12%

Statistics for Decision Making

**Question 18**

**An investment advisor believes that there is a 30% chance of making money by investing in a specific stock. If the stock makes money, then there is a 52% chance that among those making money, they would also get a dividend. Find the probability that the investor makes money but does not receive a dividend.**

18%

16%

14%

30%

**Question 19**

**A smartphone company found in a survey that 6% of people did not own a smartphone, 15% owned a smartphone only, 26% owned a smartphone and only a tablet, 32% owned a smartphone and only a computer, and 21% owned all three. If a person were selected at random, what is the probability that the person would own a smartphone only or a smartphone and computer?**

47%

42%

41%

32%

**Question 20**

**Match the terms and their definitions**

0 and 1

1 – P(E)

The occurrence of one event does not affect the occurrence of the other

Cannot occur at the same time

Probability of an event given that another event has occurred

**MATH 221 Homework Week 3**

**https://www.hiqualitytutorials.com/product/math221-homework-week-3/**

**Question 1**

**Let x represent the height of first graders in a class. This would be considered what type of variable:**

Continuous

Discrete

Lagging

Nonsensical

Statistics for Decision Making

**Question 2**

**Let x represent the inches of rain on crops in Akron, Ohio. This would be considered what type of variable:**

Continuous

Inferential

Distributed

Discrete

**Question 3**

**Consider the following table.**

Age Group | Frequency |

18-29 | 9831 |

30-39 | 7845 |

40-49 | 6869 |

50-59 | 6323 |

60-69 | 5410 |

70 and over | 5279 |

If you created the probability distribution for these data, what would be the probability of 60-69?

12.7%

13.0%

18.9%

15.2%

Statistics for Decision Making

**Question 4**

**Consider the following table.**

Weekly hours worked | Probability |

1-30 (average=22) | 0.08 |

31-40 (average=35) | 0.16 |

41-50 (average=46) | 0.72 |

51 and over (average=61) | 0.04 |

Find the mean of this variable.

41.0

49.2

42.9

44.2

**Question 5**

**Consider the following table.**

Defects in batch | Probability |

0 | 0.05 |

1 | 0.18 |

2 | 0.29 |

3 | 0.24 |

4 | 0.13 |

5 | 0.11 |

Find the variance of this variable.

1.35

2.58

1.83

2.55

**Question 6**

**Consider the following table.**

Defects in batch | Probability |

2 | 0.18 |

3 | 0.29 |

4 | 0.18 |

5 | 0.14 |

6 | 0.11 |

7 | 0.10 |

Find the standard deviation of this variable.

1.58

4.01

1.52

2.49

Statistics for Decision Making

**Question 7**

**The standard deviation of the number of video game A’s outcomes is 1.8940, while the standard deviation of the number of video game B’s outcomes is 1.6179. Which game would you be likely to choose if you wanted players to have the most choice and why?**

Game A, as the standard deviation is lower and, thus offers fewer choices in outcomes

Game A, as the standard deviation is higher and, thus offers fewer choices in outcomes

Game B, as the standard deviation is higher and, thus offers more choices in outcomes

Game B, as the standard deviation is lower and, thus offers more choices in outcomes

**Question 8**

**Ten fourth graders are randomly selected. The random variable represents the number of fourth graders who own a smartphone. For this to be a binomial experiment, what assumption needs to be made?**

The probability of owning a smartphone is the same for all fourth graders

The probability of being selected is the same for all fourth graders

All ten selected fourth graders are the same age

The probability of being a fourth grader is the same for all those selected

**Question 9**

**A survey found that 75% of all golfers play golf on the weekend. Eighteen golfers are randomly selected. The random variable represents the number of golfers that play on the weekends. What is the value of p?**

75

0.18

0.75

X, the counter

**Question 10**

**Fifty-nine percent of US adults have little confidence in their cars. You randomly select eight US adults. Find the probability that the number of US adults who have little confidence in their cars is (1) exactly three and then find the probability that it is (2) more than 6.**

(1) 0.133 (2) 0.096

(1) 0.904 (2) 0.974

(1) 0.133 (2) 0.904

(1) 0.199 (2) 0.096

Statistics for Decision Making

**Question 11**

**Say a business found that 29.5% of customers in Washington prefer grey suits. The company chooses 8 customers in Washington and asks them if they prefer grey suits. What assumption must be made for this study to follow the probabilities of a binomial experiment?**

That the probability of being a selected customer is the same for all 8 people

That those selected have similar characteristics to those in the original study

That there is a 29.3% probability of being a selected customer

That the probability of preferring grey suites is the same as preferring suits of other colors

**Question 12**

**Seven baseballs are randomly selected from the production line to see if their stitching is straight. Over time, the company has found that 89.4% of all their baseballs have straight stitching. If exactly five of the seven have straight stitching, should the company stop the production line?**

Yes, the probability of exactly five having straight stitching is unusual

No, the probability of five or less having straight stitching is not unusual

No, the probability of exactly five have straight stitching is not unusual

Yes, the probability of five or less having straight stitching is unusual

**Question 13**

**A bottling company puts 16 ounces of water bottle in each bottle. The company has determined that 94% of bottles have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 12 cans has all cans that are properly filled?**

n=12, p=0.98, x=97

n=12, p=0.16, x=1

n=16, p=0.94, x=12

n=12, p=0.94, x=12

**Question 14**

**A supplier must create metal rods that are 18.1 inches long to fit into the next step of production. Can a binomial experiment be used to determine the probability that the rods are correct length or an incorrect length?**

Yes, as each rod measured would have two outcomes: correct or incorrect

No, as there are three possible outcomes, rather than two possible outcomes

No, as the probability of being about right could be different for each rod selected

Yes, all production line quality questions are answered with binomial experiments

Statistics for Decision Making

**Question 15**

**In a box of 12 tape measures, there is one that does not work. Employees take a tape measure as needed. The tape measures are not returned, once taken. You are the 8 ^{th} employee to take a tape measure. Is this a binomial experiment?**

No, binomial does not include systematic selection such as “eighth”

Yes, you are finding the probability of exactly 5 not being broken

Yes, the probability of success is one out of 12 with 8 selected

No, the probability of getting the broken tape measure changes as there is no replacement

**Question 16**

**Eighty-two percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 7 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?**

0, 1, 2, 7

1, 2, 3, 4

1, 2, 3

0, 1, 2, 3

**Question 17**

**Seventy-six percent of products come off the line within product specifications. Your quality control department selects 15 products randomly from the line each hour. Looking at the binomial distribution, if fewer than how many are within specifications would require that the production line be shut down (unusual) and repaired?**

Fewer than 9

Fewer than 10

Fewer than 12

Fewer than 11

**Question 18**

**The probability of a potential employee passing a drug test is 91%. If you selected 15 potential employees and gave them a drug test, how many would you expect to pass the test?**

15 employees

13 employees

14 employees

12 employees

Statistics for Decision Making

**Question 19**

**The probability of a potential employee passing a training course is 86%. If you selected 15 potential employees and gave them the training course, what is the probability that 12 or more will pass the test?**

0.648

0.852

0.900

0.352

**Question 20**

**Off the production line, there is a 4.6% chance that a candle is defective. If the company selected 50 candles off the line, what is the standard deviation of the number of defective candles in the group?**

2.19

2.30

1.10

1.48

**MATH 221 Homework Week 4**

**https://www.hiqualitytutorials.com/product/math221-homework-week-4/**

**Question 1**

**The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.54 minutes and a standard deviation of 1.91. Find the probability that a randomly selected individual will take less than 6 minutes to select a shoe purchase. Is this outcome unusual?**

Probability is 0.09, which is unusual as it is less than 5%

Probability is 0.91, which is unusual as it is greater than 5%

Probability is 0.09, which is usual as it is not less than 5%

Probability is 0.91, which is usual as it is greater than 5%

**Question 2**

**Monthly water bills for a city have a mean of $108.43 and a standard deviation of $32.09. Find the probability that a randomly selected bill will have an amount greater than $155, which the city believes might indicate that someone is wasting water. Would a bill that size be considered unusual?**

Probability is 0.93, which is unusual as it is greater than 5%

Probability is 0.07, which is unusual as it is not less than 5%

Probability is 0.93, which is usual as it is greater than 5%

Probability is 0.07, which is usual as it is not less than 5%

**Question 3**

**In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally distributed variable. Find the probability that randomly selected individual would spent between 35 and 48 minutes on the treadmill.**

0.62

0.19

0.81

-0.19

Statistics for Decision Making

**Question 4**

**A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.84mm and a standard deviation of 0.35mm. Find the probability that a randomly selected tire will have a depth less than 0.24mm. Would this outcome warrant a refund (meaning that it would be unusual)?**

Probability of 0.04 and would not warrant a refund

Probability of 0.96 and would warrant a refund

Probability of 0.04 and would warrant a refund

Probability of 0.96 and would not warrant a refund

**Question 5**

**A grocery stores studies how long it takes customers to get through the speed check lane. They assume that if it takes more than 10 minutes, the customer will be upset. Find the probability that a randomly selected customer takes more than 10 minutes if the average is 7.45 minutes with a standard deviation of 2.81 minutes.**

0.636

0.018

0.818

0.182

**Question 6**

**In an agricultural study, the average amount of corn yield is normally distributed with a mean of 185.2 bushels of corn per acre, with a standard deviation of 23.5 bushels of corn. If a study included 1200 acres, about how many would be expected to yield more than 206 bushels of corn per acre?**

188 acres

226 acres

974 acres

812 acres

**Question 7**

**On average, the parts from a supplier have a mean of 31.8 inches and a standard deviation of 2.4 inches. Find the probability that a randomly selected part from this supplier will have a value between 29.4 and 34.2 inches. Is this consistent with the Empirical Rule of 68%-95%-99.7%?**

Probability is 0.68, which is consistent with the Empirical Rule

Probability is 0.95, which is inconsistent with the Empirical Rule

Probability is 0.997, which is inconsistent with the Empirical Rule

Probability is 0.68, which is inconsistent with the Empirical Rule

Statistics for Decision Making

**Question 8**

**A process is normally distributed with a mean of 10.2 hits per minute and a standard deviation of 1.04 hits. If a randomly selected minute has 13.9 hits, would the process be considered in control or out of control?**

In control as this one data point is not more than three standard deviations from the mean

In control as only one data point would be outside the allowable range

Out of control as this one data point is more than two standard deviations from the mean

Out of control as this one data point is more than three standard deviations from the mean

**Question 9**

**The candy produced by a company has a sugar level that is normally distributed with a mean of 16.1 grams and a standard deviation of 0.9 grams. The company takes readings of every 10 ^{th} bar off the production line. The reading points are 17.3, 14.9, 18.3, 16.5, 16.1, 17.4, 19.4. Is the process in control or out of control and why?**

It is in control as the values jump above and below the mean

It is out of control as one of these data points is more than 3 standard deviations from the mean

It is in control as the data points more than 2 standard deviations from the mean are far apart

It is out of control as two of these data points are more than 2 standard deviations from the mean

**Question 10**

**The toasters produced by a company have a normally distributed life span with a mean of 5.8 years and a standard deviation of 0.9 years, what warranty should be provided so that the company is replacing at most 4% of their toasters sold?**

6.8 years

4.2 years

7.3 years

4.1 years

**Question 11**

**A running shoe company wants to sponsor the fastest 3% of runners. You know that in this race, the running times are normally distributed with a mean of 7.2 minutes and a standard deviation of 0.56 minutes. How fast would you need to run to be sponsored by the company?**

6.1 minutes

8.1 minutes

8.3 minutes

6.3 minutes

**Question 12**

**The weights of bags of peas are normally distributed with a mean of 12.08 ounces and a standard deviation of 1.03 ounces. Bags in the upper 4% are too heavy and must be repackaged. What is the most that bag and weigh and not need to be repackaged?**

12.03 ounces

10.28 ounces

12.18 ounces

13.88 ounces

Statistics for Decision Making

**Question 13**

**A stock’s price fluctuations are approximately normally distributed with a mean of $26.94 and a standard deviation of $3.54. You decide to sell whenever the price reaches its highest 10% of values. What is the highest value you would still hold the stock?**

$23.40

$22.40

$31.48

$30.48

**Question 14**

**In a survey of first graders, their mean height was 49.9 inches with a standard deviation of 3.15 inches. Assuming the heights are normally distributed, what height represents the first quartile of these students?**

52.02 inches

43.60 inches

47.77 inches

46.75 inches

**Question 15**

**Hospital waiting room times are normally distributed with a mean of 38.12 minutes and a standard deviation of 8.63 minutes. What is the shortest wait time that would still be in the worst 10% of wait times?**

29.49 minutes

49.18 minutes

46.75 minutes

27.06 minutes

**Question 16**

**A machine set to fill soup cans with a mean of 20 ounces and a standard deviation of 0.1 ounces. A random sample of 34 cans has a mean of 20.02 ounces. Should the machine be reset?**

No, the probability of this outcome at 0.122, would be considered usual, so there is no problem

No the probability of this outcome at 0.421 would be considered usual, so there is no problem

Yes, the probability of this outcome at 0.878 would be considered unusual, so the machine should be reset

Yes, the probability of this outcome at 0.122, would be considered unusual, so the machine should be reset

**Question 17**

**The length of timber cuts are normally distributed with a mean of 95 inches and a standard deviation of 0.52 inches. In a random sample of 45 boards, what is the probability that the mean of the sample will be between 94.8 inches and 95.8 inches?**

0.995

0.588

0.005

0.650

Statistics for Decision Making

**Question 18**

**The Dow Jones Industrial Average has had a mean gain of 432 pear year with a standard deviation of 722. A random sample of 40 years is selected. What is the probability that the mean gain for the sample was between 200 and 550?**

0.001

0.191

0.998

0.828

**Question 19**

**Of all the companies on the New York Stock Exchange, profits are normally distributed with a mean of $6.54 million and a standard deviation of $10.45 million. In a random sample of 73 companies from the NYSE, what is the probability that the mean profit for the sample was between -2.8 million and 3.9 million?**

0.019

0.015

0.215

0.105

**Question 20**

**Doing research for insurance rates, it is found that those aged 30 to 49 drive an average of 38.7 miles per day with a standard deviation of 6.7 miles. These distances are normally distributed. If a group of 60 drivers in that age group are randomly selected, what is the probability that the mean distance traveled each day is between 38.5 miles and 39.5 miles?**

0.586

0.941

0.059

0.414

**MATH 221 Homework Week 5**

**https://www.hiqualitytutorials.com/product/math221-homework-week-5/**

**Question 1**

**From a random sample of 58 businesses, it is found that the mean time the owner spends on administrative issues each week is 21.69 with a population standard deviation of 3.23. What is the 95% confidence interval for the amount of time spent on administrative issues?**

(19.24, 24.14)

(21.78, 22.60)

(20.86, 22.52)

(20.71, 22.67)

Statistics for Decision Making

**Question 2**

**If a confidence interval is given from 43.85 up to 61.95 and the mean is known to be 52.90, what is the margin of error?**

18.10

43.85

4.25

9.05

**Question 3**

**If a car manufacturer wanted lug nuts that fit nearly all the time, what characteristics would be better?**

narrow confidence interval at high confidence level

wide confidence interval with high confidence level

wide confidence interval with low confidence level

narrow confidence interval at low confidence level

**Question 4**

**Which of the following are most likely to lead to a narrow confidence interval?**

small sample size

large standard deviation

large mean

small standard deviation

**Question 5**

**If you were designing a study that would benefit from very disperse data points, you would want the input variable to have:**

a small standard deviation

a large mean

a large margin of error

a large sample size

**Question 6**

**The 95% confidence interval for these parts is 56.98 to 57.05 under normal operations. A systematic sample is taken from the manufacturing line to determine if the production process is still within acceptable levels. The mean of the sample is 57.04. What should be done about the production line?**

Keep the line operating as it is outside the confidence interval

Stop the line as it is outside the confidence interval

Keep the line operating as it is inside the confidence interval

Stop the line as it is inside the confidence interval

Statistics for Decision Making

**Question 7**

**In a sample of 41 temperature readings taken from the freezer of a restaurant, the mean is 29.7 degrees and the population standard deviation is 2.7 degrees. What would be the 80% confidence interval for the temperatures in the freezer?**

(27.00, 32.4)

(29.16, 30.24)

(24.30, 35.10)

(31.36, 32.44)

**Question 8**

**What is the 99% confidence interval for a sample of 52 seat belts that have a mean length of 85.6 inches long and a population standard deviation of 2.9 inches?**

(84.7, 86.5)

(84.6, 86.6)

(83.1, 88.1)

(84.4, 86.8)

**Question 9**

**If two samples A and B had the same mean and standard deviation, but sample A had a larger sample size, which sample would have the wider 95% confidence interval?**

Sample B as its sample is more dispersed

Sample A as it comes first

Sample B as it has the smaller sample

Sample A as it has the larger sample

**Question 10**

**Why might a company use a lower confidence interval, such as 80%, rather than a high confidence interval, such as 99%?**

They make computer parts where they are too small for higher accuracy

They make children’s toys where imprecision is expected

They are in the medical field, so cannot be so precise

They track the migration of fish where accuracy is not as important

Statistics for Decision Making

**Question 11**

**Determine the minimum sample size required when you want to be 95% confident that the sample mean is within two units of the population mean. Assume a population standard deviation of 3.8 in a normally distributed population.**

15

13

14

12

**Question 12**

**Determine the minimum sample size required when you want to be 99% confident that the sample mean is within 0.25 units of the population mean. Assume a population standard deviation of 2.9 in a normally distributed population.**

893

892

517

365

**Question 13**

**In a sample of 10 CEOs, they spent an average of 12.9 hours each week looking into new product opportunities with a sample standard deviation of 4.9 hours. Find the 95% confidence interval. Assume the times are normally distributed.**

(11.1, 14.7)

(9.4, 16.4)

(8.0, 17.8)

(9.9, 15.9)

**Question 14**

**In a sample of 31 kids, their mean time on the internet on the phone was 36.5 hours with a sample standard deviation of 8.3 hours. Which distribution would be most appropriate to use, when we assume these times are normally distributed?**

z distribution as the population standard deviation is known

z distribution as the sample standard deviation is known

t distribution as the sample standard deviation is unknown

t distribution as the population standard deviation is unknown

**Question 15**

**Under a time crunch, you only have time to take a sample of 10 water bottles and measure their contents. The sample had a mean of 20.05 ounces with a sample standard deviation of 0.8 ounces. What would be the 90% confidence interval, when we assumed these measurements are normally distributed?**

(19.59, 20.51)

(19.25, 20.85)

(19.63, 20.47)

(18.45, 21.65)

Statistics for Decision Making

**Question 16**

**Say that a supplier claims they are 99% confident that their products will be in the interval of 50.02 to 50.38. You take samples and find that the 99% confidence interval of what they are sending is 50.00 to 50.36. What conclusion can be made?**

The supplier is more accurate than they claimed

The supplier products have a lower mean than claimed

The supplier products have a higher mean than claimed

**The supplier is less accurate than they claimed**

**Question 17**

**Market research indicates that a new product has the potential to make the company an additional $1.6 million, with a standard deviation of $2.0 million. If these estimates were based on a sample of 8 customers from a normally distributed data set, what would be the 95% confidence interval?**

(0.00, 3.27)

(-0.40, 3.60)

(0.21, 3.00)

(-0.07, 3.27)

**Question 18**

**In a sample of 28 cups of coffee at the local coffee shop, the temperatures were normally distributed with a mean of 162.5 degrees with a sample standard deviation of 14.1 degrees. What would be the 95% confidence interval for the temperature of your cup of coffee?**

(157.03, 167.97)

(157.96, 167.04)

(148.40, 176.60)

(158.12, 166.88)

**Question 19**

**In a situation where the sample size was 28 while the population standard deviation was increased, what would be the impact on the confidence interval?**

It would become wider with more dispersion in values

It would widen with more values

It would become narrower due to using the t distribution

It would become wider due to using the z distribution

Statistics for Decision Making

**Question 20**

**You needed a supplier that could provide parts as close to 76.8 inches in length as possible. You receive four contracts, each with a promised level of accuracy in the parts supplied. Which of these four would you be most likely to accept?**

Mean of 76.8 with a 99% confidence interval of 76.6 to 77.0

Mean of 76.800 with a 90% confidence interval of 76.6 to 77.0

Mean of 76.8 with a 95% confidence interval of 76.6 to 77.0

Mean of 76.800 with a 99% confidence interval of 76.5 to 77.1

**MATH 221 Homework Week 6**

**https://www.hiqualitytutorials.com/product/math221-homework-week-6/**

**Question 1**

**A consumer analyst reports that the mean life of a certain type of alkaline battery is no more than 63 months. Write the null and alternative hypotheses and note which is the claim.**

Ho: μ = 63 (claim), Ha: μ ≥ 63

Ho: μ ≤ 63 (claim), Ha: μ > 63

Ho: μ ≤ 63, Ha: μ > 63 (claim)

Ho: μ > 63 (claim), Ha: μ ≤ 63

**Question 2**

**A business claims that the mean time that customers wait for service is at most 3.5 minutes. Write the null and alternative hypotheses and note which is the claim.**

Ho: μ ≥ 3.5, Ha: μ ≤ 3.5 (claim)

Ho: μ ≤ 3.5 (claim), Ha: μ > 3.5

Ho: μ > 3.5, Ha: μ ≤ 3.5 (claim)

Ho: μ > 3.5 (claim), Ha: μ > 3.5

**Question 3**

**An amusement park claims that the average daily attendance is at least 10,000. Write the null and alternative hypotheses and note which is the claim.**

Ho: μ = 10000, Ha: μ ≤ 10000 (claim)

Ho: μ > 10000 (claim), Ha: μ = 10000

Ho: μ ≤ 10000, Ha: μ > 10000 (claim)

Ho: μ ≥ 10000 (claim), Ha: μ < 10000

Statistics for Decision Making

**Question 4**

**A transportation organization claims that the mean travel time between two destinations is about 17 minutes. Write the null and alternative hypotheses and note which is the claim.**

>Ho: μ = 17 (claim), Ha: μ ≤ 17

Ho: μ ≠ 17, Ha: μ = 17 (claim)

Ho: μ > 17, Ha: μ ≤ 17 (claim)

Ho: μ = 17 (claim), Ha: μ ≠ 17

**Question 5**

**Type I and type II errors occur because of what issue within the hypothesis testing process?**

The sample taken is not representative of the population

The math calculations were done incorrectly

The sample mean is different than the population mean

The population is not a representative subset of the sample

**Question 6**

**A scientist claims that the mean gestation period for a fox is less than 50.3 weeks. If a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted?**

There is enough evidence to support the scientist’s claim that the gestation period is less than 50.3 weeks

There is not enough evidence to support the scientist’s claim that the gestation period is 50.3 weeks

There is not enough evidence to support the scientist’s claim that the gestation period is more than 50.3 weeks

The evidence indicates that the gestation period is more than 50.3 weeks

**Question 7**

**A marketing organization claims that more than 10% of its employees are paid minimum wage. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted?**

There is sufficient evidence to support the claim that less than 10% of the employees are paid minimum wage

There is not sufficient evidence to support the claim that 10% of the employees are paid minimum wage

There is not sufficient evidence to support the claim that more than 10% of the employees are paid minimum wage

There is sufficient evidence to support the claim that more than 10% of the employees are paid minimum wage

Statistics for Decision Making

**Question 8**

**A sprinkler manufacturer claims that the average activating temperatures is at least 134 degrees. To test this claim, you randomly select a sample of 32 systems and find the mean activation temperature to be 133 degrees. Assume the population standard deviation is 3.3 degrees. Find the standardized test statistic and the corresponding p-value.**

z-test statistic = 1.71, p-value = 0.0432

z-test statistic = 1.71, p-value = 0.0865

z-test statistic = -1.71, p-value = 0.0865

z-test statistic = -1.71, p-value = 0.0432

**Question 9**

**A consumer group claims that the mean acceleration time from 0 to 60 miles per hour for a sedan is 7.0 seconds. A random sample of 33 sedans has a mean acceleration time from 0 to 60 miles per hour of 7.6 seconds. Assume the population standard deviation is 2.3 seconds. Find the standardized test statistic and the corresponding p-value.**

>z-test statistic = 1.499, p-value = 0.134

z-test statistic = 1.499, p-value = 0.067

z-test statistic = -1.499, p-value = 0.134

>z-test statistic = -1.499, p-value = 0.067

**Question 10**

**A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.8 milligrams. You find a random sample of 48 12-ounce bottles of caffeinated soft drinks that has a mean caffeine content of 32.8 milligrams. Assume the population standard deviation is 12.5 milligrams. At α=0.05, what type of test is this and can you reject the organization’s claim using the test statistic?**

Claim is null, fail to reject the null and reject claim as test statistic (-2.77) is not in the rejection region defined by the critical value (-1.96)

Claim is alternative, reject the null and support claim as test statistic (-2.77) is in the rejection region defined by the critical value (-1.64)

>Claim is null, reject the null and reject claim as test statistic (-2.77) is in the rejection region defined by the critical value (-1.96)

Claim is alternative, fail to reject the null and support claim as test statistic (-2.77) is not in the rejection region defined by the critical value (-1.64)

**Question 11**

**A computer manufacturer estimates that its cheapest screens will last less than 2.8 years. A random sample of 61 of these screens has a mean life of 2.7 years. The population is normally distributed with a population standard deviation of 0.88 years. At α=0.02, what type of test is this and can you support the organization’s claim using the test statistic?**

Claim is alternative, reject the null and support claim as test statistic (-0.89) is not in the rejection region defined by the critical value (-2.33)

Claim is alternative, fail to reject the null and cannot support claim as test statistic (-0.89) is not in the rejection region defined by the critical value (-2.05)

Claim is null, reject the null and support claim as test statistic (-0.89) is not in the rejection region defined by the critical value (-2.05)

Claim is null, fail to reject the null and cannot support claim as test statistic (-0.89) is not in the rejection region defined by the critical value (-2.33)

**Question 12**

**A pharmaceutical company claims that the average cold lasts an average of 8.4 days. They are using this as a basis to test new medicines designed to shorten the length of colds. A random sample of 106 people with colds, finds that on average their colds last 8.5 days. The population is normally distributed with a population standard deviation of 0.9 days. At α=0.02, what type of test is this and can you support the company’s claim using the p-value?**

Claim is null, reject the null and cannot support claim as the p-value (0.253) is less than alpha (0.02)

Claim is alternative, fail to reject the null and support claim as the p-value (0.126) is less than alpha (0.02)

Claim is alternative, reject the null and support claim as the p-value (0.126) is greater than alpha (0.02)

Claim is null, fail to reject the null and support claim as the p-value (0.253) is greater than alpha (0.02)

**Question 13**

**A business receives supplies of copper tubing where the supplier has said that the average length is 26.70 inches so that they will fit into the business’ machines. A random sample of 48 copper tubes finds they have an average length of 26.75 inches. The population standard deviation is assumed to be 0.15 inches. At α=0.05, should the business reject the supplier’s claim?**

No, since p>α, we reject the null and the null is the claim

Yes, since p<α, we reject the null and the null is the claim

No, since p>α, we fail to reject the null and the null is the claim

Yes, since p>α, we fail to reject the null and the null is the claim

Statistics for Decision Making

**Question 14**

**The company’s cleaning service states that they spend more than 46 minutes each time the cleaning service is there. The company times the length of 37 randomly selected cleaning visits and finds the average is 47.2 minutes. Assuming a population standard deviation of 5.2 minutes, can the company support the cleaning service’s claim at α=0.10?**

Yes, since p>α, we reject the null. The claim is the null, so the claim is not supported

No, since p>α, we fail to reject the null. The claim is the alternative, so the claim is not supported

Yes, since p<α, we fail to reject the null. The claim is the null, so the claim is not supported

No, since p<α, we reject the null. The claim is the alternative, so the claim is supported

**Question 15**

**A customer service phone line claims that the wait times before a call is answered by a service representative is less than 3.3 minutes. In a random sample of 62 calls, the average wait time before a representative answers is 3.24 minutes. The population standard deviation is assumed to be 0.40 minutes. Can the claim be supported at α=0.08?**

Yes, since test statistic is not in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported

Yes, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported

No, since test statistic is in the rejection region defined by the critical value, fail to reject the null. The claim is the alternative, so the claim is not supported

No, since test statistic is not in the rejection region defined by the critical value, fail to reject the null. The claim is the alternative, so the claim is not supported

Statistics for Decision Making

**Question 16**

**In a hypothesis test, the claim is μ≤40 while the sample of 27 has a mean of 41 and a sample standard deviation of 5.9 from a normally distributed data set. In this hypothesis test, would a z test statistic be used or a t test statistic and why?**

t test statistic would be used as the data are normally distributed with an unknown population standard deviation

t test statistic would be used as the standard deviation is less than 10

z test statistic would be used as the mean is greater than 30

z test statistic would be used as the population standard deviation is known

**Question 17**

**A university claims that the mean time professors are in their offices for students is at least 6.5 hours each week. A random sample of twelve professors finds that the mean time in their offices is 6.2 hours each week. With a sample standard deviation of 0.49 hours from a normally distributed data set, can the university’s claim be supported at α=0.05?**

Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported

Yes, since the test statistic is in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported

No, since the test statistic is not in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported

No, since the test statistic is in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported

**Question 18**

**A credit reporting agency claims that the mean credit card debt in a town is greater than $3500. A random sample of the credit card debt of 20 residents in that town has a mean credit card debt of $3600 and a standard deviation of $391. At α=0.10, can the credit agency’s claim be supported, assuming this is a normally distributed data set?**

Yes, since p-value of 0.13 is less than 0.55, reject the null. Claim is alternative, so is supported

No, since p of 0.13 is greater than 0.10, fail to reject the null. Claim is alternative, so is not supported

Yes, since p-value of 0.13 is greater than 0.10, fail to reject the null. Claim is null, so is supported

No, since p-value of 0.13 is greater than 0.10, reject the null. Claim is null, so is not supported

**Question 19**

**A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars form this company have an average gas mileage of 25.5 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set?**

Yes, since the test statistic of -1.41 is not in the rejection region defined by the critical value of -1.55, the null is rejected. The claim is the null, so is supported

Yes, since the test statistic of -1.41 is not in the rejection region defined by the critical value of -1.77, the null is not rejected. The claim is the null, so is supported

No, since the test statistic of -1.41 is close to the critical value of -1.24, the null is not rejected. The claim is the null, so is supported

No, since the test statistic of -1.41 is in the rejection region defined by the critical value of -1.77, the null is rejected. The claim is the null, so is not supported

Statistics for Decision Making

**Question 20**

**A researcher wants to determine if zinc levels are different between the top of a glass of water and the bottom of a glass of water. Many samples of water are taken. From half, the zinc level at the top is measured and from half, the zinc level at the bottom is measured. Would this be a valid matched pair test?**

No, as the zinc levels cannot be accurately measured

Yes, as long as they are all from the same faucet

No, as the measurements of top and bottom should be from the same glass

Yes, as long as there are an equal number of glasses in each group

**MATH 221 Homework Week 7**

**https://www.hiqualitytutorials.com/product/math221-homework-week-7/**

**Question 1**

**Two variables have a negative linear correlation. Does the dependent variable increase or decrease as the independent variable increases?**

Dependent variable would remain the same

Dependent variable increases

Cannot determine from information given

Dependent variable decreases

Statistics for Decision Making

**Question 2**

**What does the variable µ represent?**

The sample mean

The population mean

The sample standard deviation

The population standard deviation

**Question 3**

**A golfer wants to determine if the type of driver she uses each year can be used to predict the amount of improvement in her game. Which variable would be the explanatory variable?**

The rating of the golfer

The type of driver

The improvement in her game

The number of holes she plays

**Question 4**

**Two variables have a negative linear correlation. Is the slope of the regression line between these two variables positive or negative?**

Positive. As one variable increases, so does the other

Positive. As one variable increases, the other decreases

Negative. As one variable increases, the other decreases

Negative. As one variable increases, so does the other

Statistics for Decision Making

**Question 5**

**A value of the slope of the regression line would be given the notation of:**

M

B

R

R²

Question 6

What would be the notation for the mean of the y values?

B

Y

(x, y)

ȳ

**Question 7**

**Which of the following graphs displays the regression line of ŷ=0.75x + 3.34?**

**Question 8**

**Find the regression equation for the following data set**

x | 143 | 167 | 143 | 189 | 122 | 174 | 134 | 155 |

y | 60 | 80 | 72 | 69 | 44 | 59 | 51 | 63 |

12.16x + 0.33

Cannot be determined

0.33x + 12.16

12.16x – 0.33

**Question 9**

**A data set whose original x values ranged from 41 through 78 was used to generate a regression equation of ŷ=5.3x – 21.9. Use the regression equation to predict the value of y when x=56.**

Meaningless result

1121.1

318.7

274.9

Statistics for Decision Making

**Question 10**

**A data set whose original x values ranged from 120 through 351 was used to generate a regression equation of ŷ=0.06x + 14.2. Use the regression equation to predict the value of y when x=110.**

Meaningless result

-7.6

20.80

21.34

Question 11

Find the regression equation for the following data set

x | 7 | 8 | 5 | 9 | 4 | 3 | 9 | 6 | 7 | 8 |

y | 4 | 2 | 8 | 3 | 7 | 9 | 3 | 5 | 6 | 9 |

-11.20x – 0.85

0.85x + 11.20

11.20x – 0.85

11.20x – 0.85

**Question 12**

**A data set whose original x values ranged from 137 through 150 was used to general a regression equation of ŷ=-4.5x + 51. Use the regression equation to predict the value of y when x=145.**

-601.5

-619.5

-703.5

Meaningless result

**Question 13**

**If the linear correlation coefficient is 0.482, what is the value of the coefficient of determination?**

0.232

-0.982

-0.232

0.982

**Question 14**

**If the linear correlation coefficient is -0.368, what is the value of the coefficient of determination?**

-0.135

0.135

0.736

0.184

**Question 15**

**If the coefficient of determination is 0.233, what percentage of the data about the regression line is explained?**

5.43%

76.7%

46.6%

23.3%

**Question 16**

**If the coefficient of determination is 0.298, what percentage of the data about the regression line is unexplained?**

6.9%

26.2%

70.2%

73.8%

Statistics for Decision Making

**Question 17**

**If the independent variables explained less than 50% of the variation in the dependent variables, which of the following would be true?**

The coefficient of determination is below 0.5

There are two independent variables

There are two dependent variables

The coefficient of determination is above 0.5

**Question 18**

**The equation used to predict how tall a dog will be as an adult is ŷ=4.5 + 0.7x _{1} + 0.55x_{2}, where x_{1} is the height of the mother and x_{2} is the height of the father. Use this equation to predict the height of a puppy whose mother is 41.3 inches tall and whose father is 44.9 inches tall.**

58.65 inches

53.61 inches

58.11 inches

43.10 inches

**Question 19**

**The equation used to predict how long it will take to receive a package through the mail is ŷ=0.5 + 0.02x _{1} + 0.85x_{2}**

**days, where x**

_{1}is the distance to travel and x_{2}is the weight of the package. Use this equation to predict the how long it will take to receive a package that is 224 miles away and weighs 2.2 pounds.190.9 days

6.9 days

113.1 days

6.4 days

**Question 20**

**The equation used to predict how long a cold will last is ŷ=-1.8 + 0.09x _{1} + 3.2x_{2 }– 1.9x_{3}, where x_{1}**

**is person’s temperature on the first day, x**

_{2}is number of people seen each day, and x_{3}is the amount of sleep the person gets. Use this equation to predict how long a cold will last with a temperature of 100.4 degrees, an average of 4 people seen each day, and 6 hours of sleep.12.3 days

7.0 days

8.6 days

10.5 days

Statistics for Decision Making

**MATH 221 Discussions Week 1-7 All Students Posts 474 Pages**

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**MATH 221 Descriptive Statistics Discussions Week 1 All Students Posts 60 Pages**

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If you were given a large data set, such as the sales over the last year of our top 100 customers, what might you be able to do with these data? What might be the benefits of describing the data?

Alternative: Look for examples of descriptive statistics in the news or on websites. Then post a link to that publication or site, note the statistic used and determine if it was an appropriate use of that statistic.

Please select a topic from this list so we can continue our discussion of descriptive statistics.

- Definition of population and sample. Provide examples.
- Definition of parameter and statistic. Provide examples.
- What are the various levels of measurement used in statistics? Provide examples.
- Describe the concept of qualitative and quantitative data. Provide examples.
- What is an observational study?
- What is an experiment?
- Describe a sampling method. What bias could this method introduce to the study?
- Describe the definition for mean, median and mode.
- What is a box-and-whisker plot?
- Describe the concept of census and sampling. Provide examples…

**MATH 221 Probabilities in Real World Discussions Week 2 All Students Posts 73 Pages**

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Look online and find an article published within the past 4 weeks that includes a reference to probabilities, means, or standard deviations. These articles might be discussing weather events, investing outcomes, or sports performance, among many other possible topics.

Your first post should include a summary of the article and what numbers you are highlighting from that article. Also include a link to the actual article. In your replies to other students, describe specific decisions that the statistic might influence and whether a different statistic might be more appropriate.

These are all potential distributions out there. From here, some special cases are developed to explain those data sets. Thus, the need to combine two of the distributions. Each of the distributions has its own formula(s) for probability and sometimes for descriptive statistics. In class we will mainly work with binomial, geometric, Poisson and normal. The rest will leave for more advanced statistics.

Also, these distributions will break into discrete or continuous cases. In later weeks, we will talk about the difference of these two data sets…

Statistics for Decision Making

**MATH 221 Discrete Probability Variables Discussions Week 3 All Students Posts 60 Pages**

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For this discussion you will use technology to create a short 1-2 minute multimedia post/presentation.

Suggestions: Narrated PowerPoint, recorded video (.mp4), Screencast-O-Matic (.mp4), or a similar tool of your choice. Video can be recorded directly within a post as well, but make sure to plan out in advance what you are going to say/show. There should be a visual component as well as audio, so if you are using a webcam for the video that only shows you speaking, please attach your PowerPoint slide(s) (or screenshot images of them) to the post as well so everyone can see them.

In your short presentation, you will be describing an example that uses discrete probabilities or distributions. Provide an example that follows either the binomial probabilities or any discrete probability distribution, and explain why that example follows that distribution. In your responses to other students, make up numbers for the example provided by that other student, and ask a related probability question. Then show the work (or describe the technology steps) and solve that probability example.

For more information about Narrated PowerPoint, access the Student Resources section of Course Resources under the Introduction & Resources module heading, and look for the heading that corresponds to the tool you want to use. For all media posts in this course, please include a brief written synopsis to inform your classmates what the main point or purpose is that the linked, attached, or embedded media addresses.

We need to meet two conditions for a distribution to be considered a probability distribution.

- a) All probabilities have to be between 0 and 1,
- b) Sum of all probabilities has to be 1.

There are three characteristics of a binomial experiment:

- There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter
*n*denotes the number of trials. - There are only two possible outcomes, called
*success*and*failure*, for each trial. The outcome that we are measuring is defined as a*success*, while the other outcome is defined as a*failure*. The letter*p*denotes the probability of a success on one trial, and*q*denotes the probability of a failure on one trial.*p*+*q*= 1. - The
*n*trials are independent and are repeated using identical conditions. Because the*n*trials are independent, the outcome of one trial does not help in predicting the outcome of another trial. Another way of saying this is that for each individual trial, the probability,*p*, of a success and probability,*q*, of a failure remain the same. Let us look at several examples of a binomial experiment…

**MATH 221 Interpreting Normal Distributions Discussions Week 4 All Students Posts 77 Pages**

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Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?

Sample mean = 115

Population mean = 100

Standard deviation = 15

Sample size = 3

We can use formula Z = (x-µ)/(Ó/√n)

Z = (115-100)/(15/√3)

Z= 1.7320

P (X >=115) = P (z >1.732) = 1 – 0.9582 = 0.0418

The probability of sample of 3 with a mean of 115 is 4.18%

An event that occurs with a probability of 0.05 (5%) or less is typically considered unusual.

Therefore, this would be an unusual scenario….

**MATH 221 Confidence Interval Concepts Discussions Week 5 All Students Posts 68 Pages**

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Look in the newspapers, magazines, and other news sources for results of a survey or poll that show the confidence interval, usually shows as a +/- some amount. Describe the survey or poll and then describe the interval shown. How does knowing the interval, rather than just the main result, impact your view of the results?

To study applies, we would need to determine what we are measuring: weight, size, diameter, surface area, etc. To build a confidence interval we will need: statistic __+__ (critical value)(standard deviation).

What aspect of making a magazine better is the 54% measuring? Could we safely make decisions based on a survey that asks a reader population? How could the participation selection be made to reduce bias in the survey?…

Statistics for Decision Making

**MATH 221 Hypotheses in the Real World Discussions Week 6 All Students Posts 66 Pages**

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Consider a business of any type. What is a situation where a hypothesis test might help make a decision? Describe the situation. Then you or someone in a reply can make up numbers for that situation and someone else can solve it.

Hypothesis testing is the foundation for inferential statistics. We can use this process to make inferences about populations. It is a simple process. However, there are various details that need to be examined before coming up with a conclusion. Here is a list of the steps:…

Hypothesis testing has a lot of different cases you have to consider which makes it seem harder than what it is. The sample size will vary. Perimeters will be different but the overall hypothesis testing will be the same. Hypothesis is a claim that we want to test. Null Hypothesis is the currently accepted value for a parameter. When this permanent gets tested its call the alternative hypothesis. Also called the research hypothesis. This involves the claim to be tested. This usually happens when you are trying to test a theory to see if it’s still accurate…

**MATH 221 Regression Discussions Week 7 All Students Posts 70 Pages**

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This week we will talk about correlation and regression. These are two important concepts that will help us make better decisions about what a data set is telling us.

Here is my 3 min talk about these:…

Other topics for you to discuss with us would be:

- Examples of scatter diagrams and how to use them to determine how strong the relationship is between the independent and dependent variables.
- What is the correlation coefficient of a data set and how can we interpret its meaning?
- Interpret the slope and intercept of the regression equation.
- What is the coefficient of determination of a data set and how can we interpret its meaning?
- How can we calculate the regression equation of a data set and how can we predict the value of one variable (Y) based on a set of independent variables?
- What are independent and dependent variables?…

**The Final Exams are located under the two links listed below**

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Statistics for Decision Making

DeVry